Similar Triangle

Drill or pre-test Problem 1:In the triangle ABC shown below, A'C' is parallel to AC. Find the length y of BC' and the length x of A'A.

2.The picture below shows a right triangle. Find the length of h; the height drawn to the hypotenuse.

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If two shapes are similar, one is an enlargement of the other. This means that the two shapes will have the same angles and their sides will be in the same proportion (e.g. the sides of one triangle will all be 3 times the sides of the other etc.). Triangles ABC is similar to triangles XYZ written as ABC ~ XYZ, under the corresponding A X,B Y, C Z, if and only if i. All pair of corresponding angles are congruent. ii. All pair of corresponding sides are proportional.

Consider the following figures: B Y A C X Z We say that ABC ~ XYZ if and only if Angles A is congruent to angle X, angle B is congruent to angle Y, angle C is congruent to angle Z.

example Given that ABC ~ DEF. find the values of x and y. B E 3 4 X 8 A C D F View solution

Solution Since the corresponding sides are proportional, we have. AB BC AC DE EF DF X 8 y X 2 y x=6;y =10

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Activity: # 1 1. The triangles shown below are similar. Find the exact values of a and b shown on the picture below.

Activity:# 2 2. Consider the picture shown below (a) Use the Pythagorean Theorem to.nd the value of a. (b) Prove that the triangles ABE and ACD are similar. (c) Use similar triangles to.nd the value of x. (d) Find the value of b.

Assessment no.#1 Problem 1. A person is standing 40 Ft. away from a street light that is 30 Ft. tall. How tall is he if his shadow is 10 Ft. long?

Assessment. #2 Problem 2: A research team wishes to determine the altitude of a mountain as follows: They use a light source at L, mounted on a structure of height 2 meters, to shine a beam of light through the top of a pole P' through the top of the mountain M'. The height of the pole is 20 meters. The distance between the altitude of the mountain and the pole is 1000 meters. The distance between the pole and the laser is 10 meters. We assume that the light source mount, the pole and the altitude of the mountain are in the same plane. Find the altitude h of the mountain.

Answer keys

Reference

Reference

Solution no.#1 activity card

Solution no.#2 activity card