Home

# How many altitudes can a triangle

### How many altitudes can a triangle have

1. How many altitudes can a triangle have? Every triangle has three bases (any of its sides) and three altitudes (heights).Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side Now, using the area of a triangle and its height, the base can be easily calculated as Base = [(2 × Area)/Height] Altitudes of Different Triangles. About altitude, different triangles have different types of altitude. Below is an overview of different types of altitudes in different triangles. Altitude of an Obtuse Triangle

what is altitude? Prove that the bisector of the vertical angle of an isosceles triangle is perpendicular to the base. Show the shape of a triangle. How many sides, angles and vertices are there in a triangle? In the triangle given below Name: (i) The side opposite to vertex Q (ii) Angle opposite to side PQ. Look at the figures given below Best Answer (c) An altitude has one end point at a vertex of the triangle and the other on the line containing the opposite side. Then we can say that a triangle have 3 altitudes Step-by-step explanation: Since all triangles have three vertices and three opposite sides, all triangles have three altitudes. The three altitudes of any triangle (or lines containing the altitudes) intersect at a common location called the orthocentre A triangle has three altitudes. It helps to find out the area of the triangle. We are using altitudes to find the trigonometric ratios. The point where the three altitudes of a triangle intersect is known as the orthocenter The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle. A triangle has 3 altitudes. New questions in Math The base and height ofthe triangle are in the ratio 3:2 and its area is 108 cm. Find its baseand height

There are many ways to find the height of the triangle. The most popular one is the one using triangle area, but many other formulas exist: Given triangle area. Well-known equation for area of a triangle may be transformed into formula for altitude of a right triangle: area = b * h / 2, where b is a base, h - height. so h = 2 * area / b Every triangle has three bases (any of its sides) and three altitudes (heights). Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side) (Figure 1). Figure 1 Three bases and three altitudes for the same triangle Altitude of a Triangle An altitude of a triangle is the perpendicular segment from a vertex of a triangle to the opposite side (or the line containing the opposite side). An altitude of a triangle can be a side or may lie outside the triangle The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle. In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex)

A triangle can have three altitudes. The altitudes can be inside or outside the triangle, depending on the type of triangle. The altitude makes an angle of 90° to the side opposite to it. The point of intersection of the three altitudes of a triangle is called the orthocenter of the triangle Every triangle has three altitudes. Think of building and packing triangles again. You would naturally pick the altitude or height that allowed you to ship your triangle in the smallest rectangular carton, so you could stack a lot on a shelf. Altitude for side U D U D (∠G ∠ G) is only 4.3 cm 4.3 c m An altitude of a triangle is a line which passes through a vertex of a triangle, and meets the opposite side at right angles. For more on this see Altitude of a Triangle. The three altitudes of a triangle all intersect at the orthocenter of the triangle. Se An altitude of a triangle is the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side. An altitude can lie inside, on, or outside the triangle. Every triangle has three altitudes. The lines containing the altitudes are concurrent and intersect at a point called the orthocenter of the triangle The altitude of a triangle is a line segment from a vertex that is perpendicular to the opposite side. A triangle has three altitudes. The point of concurrency is called the orthocenter. The orthocenter can be inside, on, or outside the triangle based upon the type of triangle. The Altitudes of a Triangle. This video defines an altitude and.

### Altitude of a Triangle - Definition, Formulas and Example

1. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles. asked Mar 28, 2020 in Triangles by Sunil01 ( 67.6k points
2. The altitude of a triangle is a line from a vertex to the opposite side, that is perpendicular to that side, A triangle therefore has three possible altitudes. The altitude is the shortest distance from a vertex to its opposite side. The word 'altitude' is used in two subtly different ways
3. For a complete lesson on median, altitude, and perpendicular bisector, go to https://www.MathHelp.com - 1000+ online math lessons featuring a personal math t..

### how many altitudes can a triangle have - Mathematics

• Altitude (height) of a triangle means, perpendicular distance between its vertex & its opposite side. A triangle has 3 vertices, so it has 3 different altitudes
• Medians and Altitudes of Triangles DRAFT. 10th - 12th grade. 3 times. 80% average accuracy. 5 months ago. brookepaiva2021_69792. 0. Save. Edit. Edit. The altitude can be inside or outside, even the legs of a right triangle. The altitude can only be inside. The altitude can only be outside. Neither. Tags
• how many altitudes can one triangle have? Share with your friends. Share 6. Dear Student! Here is the answer to your question. An altitude of a triangle is a line through a vertex and perpendicular to side opposite to the vertex. Since a triangle has 3 vertices, therefore, it has 3 altitudes
• concurrency of the altitudes of a triangle. 5. How many altitudes does a triangle have? Explain. One altitude can be drawn from each vertex of a triangle, so every triangle has three altitudes. 6. Name the altitudes of ABC. 7. What is the orthocenter of ABC? _ AX; _ BY ; _ CZ pointW median altitude

### How many altitudes can a triangle have - Entrance

Orthocenter--The common intersection of the three lines containing the altitudes. This normally labeled H. How does one construct an orthocenter? Figure 1 illustrates how the orthocenter can be found. Figure 1. Now that the orthocenter is defined, let us find the orthocenter of the three interior triangles, triangles HAB, HBC, and HAC Definition. altitude. An altitude of a triangle is a line segment from a vertex and is perpendicular to the opposite side. It is also called the height of a triangle Definitions: An altitude of a triangle is a line segment through the vertex and perpendicular to the base. All three altitudes intersect at the same point called orthocenter. Right Triangle - has a 90 degree angle, altitudes meet at the vertex of the right angle Acute Triangle - has an angle less than 90 degrees, altitudes meet inside the triangle Obtuse Triangle - has an angle more than 90.

Altitudes are defined as perpendicular line segments from the vertex to the line containing the opposite side. In each triangle, there are three triangle altitudes, one from each vertex. In an acute triangle, all altitudes lie within the triangle. In a right triangle, the altitude for two of the vertices are the sides of the triangle No. Only 2 altitudes can intersect at a point. * * * * * True but even they do not meet in the interior. The altitudes of a right angles triangle meet at the right angled vertex. The vertex is at. The other leg of the right triangle is the altitude of the equilateral triangle, so solve using the Pythagorean Theorem: a2 + b2 = c2 a 2 + b 2 = c 2. a2 + 122 = 242 a 2 + 12 2 = 24 2. a2 + 144 = 576 a 2 + 144 = 576. a2 = 432 a 2 = 432. a = 20.7846 yds a = 20.7846 y d s. Anytime you can construct an altitude that cuts your original triangle.

There is no symmetry line in it. Acute, obtuse, or right-angle interior angles exist in a scalene triangle. Q.5. How many altitudes does a scalene triangle have? Ans: A scalene triangle has three altitudes. We hope this detailed article on the scalene triangle formulas helped you in your studies How many altitudes can a triangle have? (a) 1 (b) 2 (c) 3 (d) 4. Answer/Explanation. Answer: (c) Explanation : Draw altitudes and count. 13. The total measure of the three angles of a triangle i Theorem 1. If in a triangle the two altitudes are of equal length, then the triangle is isosceles. Proof. Let ABC be a triangle with altitudes AD and BE of equal length ( Figure 1 ). We need to prove that the sides AC and BC are of equal length. Consider the triangles ADC and BEC. They are the right triangles with the common angle ACB

The altitude of a triangle, or height, is a line from a vertex to the opposite side, that is perpendicular to that side. It can also be understood as the distance from one side to the opposite vertex. Every triangle has three altitudes (h a, h b and h c), each one associated with one of its three sides You can get extra practice finding triangle altitudes with this quiz and worksheet. In these assessments, you will be shown pictures and asked to identify the different parts of a triangle. Existence of the orthocenter in many different ways (now 22). In any triangle the three altitudes meet in a single point known as the orthocenter of the triangle Theorem 8-5: If an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other. What is the geometric mean of 4 and 9? Answer and Explanation: The geometric mean between 4 and 9 is 6 How many distinct triangles can be constructed if mOA = 30, b = 12, and a = 7? A. 1 B. 2 C. 3 D. 0 8. How many distinct triangles may be constructed if a point at the airport is 32 at an altitude of 8,000 feet. A second airplane is approaching the same airport from due west, with an angle of depressio

Proof of the Law of Cosines. To show how the Law of Cosines works using the relationship c 2 = a 2 + b 2 - 2ab·cos(C) (the other two relationships can be proven similarly), draw an altitude h from angle B to side b, as shown below.. Altitude h divides triangle ABC into right triangles AEB and CEB 12.1.3 Altitudes of a Triangle In ABC, the line AL is the perpendicular drawn from vertex A to the opposite side BC. (Fig. 12.14). Fig. 12.14 Perpendicular drawn from a vertex of a triangle to the oposite side is called its altitude. How many altitudes can be drawn in a triangle? There are three vertices in a triangle, s Expert Answer: Yes, the above given statement is true in case of a right-angled triangle where two altitudes of the triangle are two of its sides. This can be illustrated by the following figure. Here, since AC is perpendicular to BC and vice-versa, both AC and BC are the sides as well as the altitudes of ABC Two of the altitudes of the scalene triangle A B C have lengths 4 a n d 1 2, If the length of the third altitude is also an integer, then its greatest value can be_____. A How many altitudes can a triangle have? (a) 1 (b) 2 (c) 3 (d) 4. 13. The total measure of the three angles of a triangle is (a) 360. The altitudes of an isosceles triangle can be found as follows: Knowing the base {eq}B {/eq} and the height {eq}H {/eq} of the triangle can use right triangle relationships to solve for h. 14.975 sin( 15 ) h a h hypotenuse opposite ° = = = Solve for h h = 14.975 sin( 15 °) ≈ 3.876 The UFO is at an altitude of 3.876 miles. In addition to solving triangles in which two angles are known, the law of sines can b In a right triangle with hypotenuse 10, the altitude perpendicular to the hypotenuse can be 6. Why some people say it's true: One of the legs of a right triangle can have a length of 6 (from the Pythagorean triple 6-8-10) and a leg can be the altitude of the triangle. Why some people say it's false: It's impossible

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. Every triangle has three altitudes. An altitude can be inside, outside, or on the triangle. In the diagram of ABC, the three altitudes are _ AX , _ BZ , and _ CY . Notice that two of the altitudes are outside the triangle Using the Law of Sines to Solve Obliques Triangles. In any triangle, we can draw an altitude, a perpendicular line from one vertex to the opposite side, forming two right triangles.It would be preferable, however, to have methods that we can apply directly to non-right triangles without first having to create right triangles Medians and Altitudes of Triangles. How Do You Use the Centroid to Find Segment Lengths in a Triangle? When you're given the centroid of a triangle and a few measurements of that triangle, you can use that information to find missing measurements in the triangle! This tutorial shows you how it's done Properties of Altitude of Triangle. Every triangle can have 3 altitudes i.e., one from each vertex as you can clearly see in the image below. All the 3 altitudes of a triangle always meet at a single point regardless of the shape of the triangle

### How many altitudes can a triangle have? - Brainly

How to calculate Altitude of an equilateral triangle using this online calculator? To use this online calculator for Altitude of an equilateral triangle, enter Side (S) and hit the calculate button. Here is how the Altitude of an equilateral triangle calculation can be explained with given input values -> 7.794229 = (sqrt(3)*9)/2 To use this online calculator for Altitude/height of a triangle on side c given 3 sides, enter Side A (S a), Side B (S b) and Side C (S c) and hit the calculate button. Here is how the Altitude/height of a triangle on side c given 3 sides calculation can be explained with given input values -> 6.998884 = sqrt((8+7+4)*(7-8+4)*(8-7+4)*(8+7-4))/(2*4) Example: In triangle PQR with vertices P(-5, 3) Q(3, 7) and R(1, -3), find the equation of median RM. Steps to Find the Altitude of a Triangle: -Find the slope of the segment that the altitude will intersect. -Calculate the negative reciprocal of this slope. This will be the slope of the altitude Using the converse of ceva's theorem it can be proved that the three altitudes are concurrent in acute and obtuse triangles. But it is kind of obvious to see why the three altitudes of a right angled triangle will have to intersect at a single point, and why that point happens to be the vertex of the right angle

### Altitude of a Triangle: Definition, Formulas for All

• 3. Draw obtuse triangle OBT with obtuse angle O. Construct altitude BU. In an obtuse triangle, an altitude can fall outside the triangle. To construct an altitude from point B of your triangle, extend side OT. In an obtuse triangle, how many altitudes fall outside the triangle and how many fall inside the triangle? 4
• Who said the hypotenuse was the base? Why can't the altitude be equal to one side of the triangle? This is a 3-4-5 right angled triangle. Or, to be precise: a 6-8-10 triangle. Hypotenuse is 10 inches, altitude (or height) is 6 inches, so the base is 8 inches. Area is: 1/2 * (6) * (8) = 24 square inches
• Right Triangles. Altitudes. An altitude of any triangle is a segment that extends from a vertex to the opposite side (or an extension of the opposite side) and is perpendicular to that side. The dashed segments, , in the following figures are altitudes of the triangles: In the special case of a right triangle, each leg is an altitude perpendicular to the other leg, and there is a third.

An altitude of a triangle is the line segment drawn from a vertex of a triangle, perpendicular to the line containing the opposite side. (i) PS is an altitude on side QR in figure. (ii) AD is an altitude, with D the foot of perpendicular lying on BC in figure. (iii) The side PQ, itself is an altitude to base QR of right angled PQR in figure We can draw infinitely many lines passing through a single point. And so it only makes sense that the concept of 'the' Euler line is associated only with non-equilateral triangles. Now for those of you reading this who don't know about these four centers of a triangle, let me quickly give a short description of each one of them We can prove this by using the Pythagorean Theorem as follows: ⇒ a 2 + b 2 = c 2 ⇒ 3 2 + 4 2 = 5 2 ⇒ 9 + 16 = 25. 25 = 25. A 3-4-5 right triangle has the three internal angles as 36.87 °, 53.13 °, and 90 °. Therefore, a 3 4 5 right triangle can be classified as a scalene triangle because all its three sides lengths and internal angles.

### How many altitudes can triangle have - Brainly

An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.. Acute and obtuse triangles are the two. Interior angles. If you are given one interior angle of an isosceles triangle you can find the other two. We know that the interior angles of all triangles add to 180°. So the two base angles must add up to 180-40, or 140°. Since the two base angles are congruent (same measure), they are each 70° How many angle bisectors can there be? Up to 3. Every triangle has _______ which will _______ intersect in the same point. 3 angle bisectors; always. Incenter. Same distance from all 3 sides of the triangle; angle bisector reference; place where 3 angle bisectors intersect. Angle bisector theorem. If a point lies on the angle bisector, then the.  ### Height of a Triangle (Altitude)

• The altitude and hypotenuse. As you can see in the picture below, this problem type involves the altitude and 2 sides of the inner triangles ( these are just the two parts of the large outer triangle's hypotenuse) .This lets us set up a mean proportion involving the altitude and those two sides (see demonstration above if you need to be convinced that these are indeed corresponding sides of.
• Another special segment in a triangle is the perpendicular bisector. The perpendicular bisectors of a triangle may meet inside, outside, or on the triangle. Kurt is trying to label an altitude, median, and angle bisector for this triangle. How many special segments does a triangle have? five special segment
• The many ways to construct a triangle III. A right triangle is well defined by a leg and an angle. Therefore, starting with an angle A, we may first construct triangle AH_ {c}C to obtain vertex C, and, in a similar manner, the triangle AH_ {b}B to obtain vertex B. Construct an arc (part of a circle) subtending segment BC = a such that for every.
• To find the number of squares we will divide the base s by the side of the square a and subtract 1 from it = s/a - 1. Then it will leave us another isosceles triangle with base (s - a) which will accommodate one less square than the previous row below it which we can calculate in the following way −. Squares in next row = (s - a)/a - 1.
• Note: There are 1 anagrams of the word altitude. Anagrams are meaningful words made after rearranging all the letters of the word. Search More words for viewing how many words can be made out of them Note There are 4 vowel letters and 4 consonant letters in the word altitude. A is 1st, L is 12th, T is 20th, I is 9th, U is 21th, D is 4th, E is.
• Point H is the point of intersection of the altitudes in acute triangle ABC. Given CH=AB, find m∠ACB, in degrees. Point H is the point of intersection of the altitudes in acute triangle ABC. Given CH=AB, find m∠ACB, in degrees. Categories English. Leave a Reply Cancel reply

### Altitudes Medians and Angle Bisector

big rectangle is triangle ABC? Lemma 2. The area of an acute triangle ABC is half of its base x height: Area of an acute triangle equals: x altitude) = (base height). Definition 2. Let CH be the altitude in triangle ABC. Point H is called the foot of the altitude, or the foot of the perpendicular from C to AB For a more, see orthocenter of a triangle. The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle Draw a line segment (called the altitude) at right angles to a side that goes to the opposite corner. Where all three lines intersect is the orthocenter: Note that sometimes the edges of the triangle have to be extended outside the triangle to draw the altitudes

You can put this solution on YOUR website! Checking, we find that 15^2 +20^2 =25^2therefore this is a rt triangle, with legs 15, and 20, and hypotenuse 25. On a right triangle, the legs are also altitudes, so 15, and 20 are altitudes Given right triangle ABCABC with altitude BDdrawn to hypotenuse AC. If BC=6 and DC=3, what is the length of AC? The volume of a cone is 37x* cubic units and its height is x units Triangle circumference with two identical sides is 117cm. The third side measures 44cm. How many cms do you measure one of the same sides? Draw a Draw a triangle ABC, if you know: alpha = 60° side b = 4 cm side a = 10 cm; Medians 2:1 Median to side b (tb) in triangle ABC is 12 cm long. a Triangle Calculator. Please provide 3 values including at least one side to the following 6 fields, and click the Calculate button. When radians are selected as the angle unit, it can take values such as pi/2, pi/4, etc. A triangle is a polygon that has three vertices The Questions and Answers of How many medians can a triangle have? are solved by group of students and teacher of Class 8, which is also the largest student community of Class 8. If the answer is not available please wait for a while and a community member will probably answer this soon

triangle below? 9 An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. Every triangle has three altitudes. An altitude can be inside, outside, or on the triangle. The point of concurrency is called the orthocenter. 10 (No Transcript) 11 Find the orthocenter of ?XYZ with vertices X(3 The sides of a triangle are 15, 20, and 2 Find the sum of the altitudes. The number 96 can be expressed as the difference of perfect squares x In the figure, ci Junior Exam March 14, 2012 Page 1 of 6 1 Basic Properties. Because the equilateral triangle is, in some sense, the simplest polygon, many typically important properties are easily calculable. For instance, for an equilateral triangle with side length. The altitude, median, angle bisector, and perpendicular bisector for each side are all the same single line Given: Right ABC as shown where CD is an altitude of the triangle. We prove that a^2+b^2=c^2. Because ABC and CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA A pseudo right triangle. We explore more properties of triangles whose side-lengths satisfy a modified Pythagorean identity: (1) Unsurprisingly, such triangles mirror many of the properties of right triangles, with minor differences. So, for the time being, we're giving them the pseudonym pseudo right triangles Types of Isosceles Triangles. There are four types of isosceles triangles: acute, obtuse, equilateral, and right. An acute isosceles triangle is a triangle with a vertex angle less than 90°, but not equal to 60°.. An obtuse isosceles triangle is a triangle with a vertex angle greater than 90°.. An equilateral isosceles triangle is a triangle with a vertex angle equal to 60° Median of an Obtuse Triangle. Point of concurrency 'P' or The three medians of an obtuse, acute, and a right triangle always meet inside the triangle. - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 12c3e7-YTM4

### Altitude of a Triangle - Varsity Tutor

5. Can the altitude and median be same for a triangle? ( Hint : For Q.No. 4 and 5, investigate by drawing the altitudes for every type of triangle). Answer: Yes, the altitude and median can be the same in a triangle. for example, consider an equilateral triangle, the median which divides the side in equal is also perpendicular to the side and hence the altitude and the median is the same ---> b = 8, which is the altitude to the base = 12 . The area of a triangle can be found using the formula: A = ½ · b · h. The base of the triangle = 12 and the height = 8 ---> A = ½ · 12 · 8 = 48 . Now, the area of the triangle on the left side of the triangle is one-half the total area = 24 An obtuse triangle is a triangle in which one of the interior angles is greater than 90°. It has one of its vertex angles as obtuse and other angles as acute angles i.e. when one angle measures more than 90°, the sum of the other two angles is less than 90°. An obtuse triangle can also be called an obtuse-angled triangle point of intersection. It is interesting that all three altitudes are coincident at the same point, but once this is established, only two altitudes are needed to locate the orthocenter. 2. When the triangle is acute, the orthocenter is located in the interior of the triangle because the feet of the altitudes lie on the sides of the triangle 3)A triangle with integer sides has perimeter 12. How many such non-congruent triangles are there? (A 3-4-5 triangle is considered congruent to a 3-5-4 triangle because we can reflect and rotate the triangles until they match up.) 4)The distance from Capital City to Little Village is 660 miles

Sure. If one of the base angles is more than 90 degrees, then the altitude (height) is outside the triangle. Yes. This only occurs with an obtuse triangle. Because an altitude is a line drawn from. 1) You can tile the plane with triangle with sides equal to the medians, then draw a few lines to get a triangle that has those medians. Some people are average, some are just mean. 2) Make a triangle from the altitudes, get the altitudes from that triangle, use those to make another triangle, then scale that to the right size An altitude of a triangle can be inside or outside the triangle, or it can be a side of the triangle. Altitude of a Triangle. Concurrency of Altitudes Theorem Acute Triangle Obtuse Triangle Right Triang Altitude of a Triangle. Share this link with a friend: Copied! Students who viewed this also studied Determine how many triangles can be drawn. Calculate, then label, all side lengths to the nearest tenth and all interior angles to the nearest degree. a= 2.1 cm, c= 6.1 cm, <A=20 degrees. Isn't height c sin A and therefore h=2.1 cm and therefore only 1 90 degree triangle is possible The segment that was drawn as you dragged the slider is called an altitude. This altitude was drawn to the hypotenuse. How many right triangles did this altitude split the original right triangle into? What does the special movement of the red and green angles imply about these 2 smaller right triangle

Circumcenter of a right triangle Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization That means all three triangles are similar to each other. Theorem 8-5: If an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other. The proof of Theorem 8-5 is in the review questions The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle. A) 24 B) 4 In general, altitudes, medians, and angle bisectors are different segments.In certain triangles, though, they can be the same segments.In Figure , the altitude drawn from the vertex angle of an isosceles triangle can be proven to be a median as well as an angle bisector

Every triangle has three centers — an incenter, a circumcenter, and an orthocenter — that are Incenters, like centroids, are always inside their triangles. Triangles have amazing properties! Among these is that the angle bisectors, segment perpendicular bisectors, medians and altitudes all meet with the Lesson 1 - Area, Parallelogram, Triangle 4 200 feet 300 feet 28. The space shuttle orbited the earth 20 times at an altitude of 280 miles. If the diameter of the earth is 8000 miles, how many miles did the space shuttle travel? 29. If a greyhound dog needs a training run of 3 miles, how many times will it need to run around the track 8: Area. 8.1 A=½bh. In Euclidean Geometry, the area of a triangle is calculated by multiplying the length of any side times the corresponding height, and dividing the product by two (A=½bh). The example below illustrates this calculation in Hyperbolic Geometry. Figure 8.1a: Altitudes of a Triangle. Triangle ABC is a Scalene triangle Geometry: Chapter 5- inequalities of one triangle, inequalities of two triangles, perpendicular bisectors, medians, altitudes, angle bisectors. exterior angle inequality. angle- side inequalities. triangle inequality theorem. hinge theorem. the measure of an exterior angle of a triangle is greater than    