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Guideline:DRILLMOTIVATIONSIMILAR TRIANGLESVIDEO OF SIMILAR TRIANGLESActivity cardAssessment cardAnswer keyReference Drill or pre-testProblem 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.

My motivation is I'm not sure, but I think it was the desire to study the similar triangles " geometry of surfaces -- e.g. to study a triangles as an object in its own right, My motivationChoose wisely 1. A.29.25

B.25.26

C.26.25

D.23.242.A.H= 60 B. H= 30 C. H= 56 D. H= 10

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

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

ACTIVITY CARDASSESMENT CARD1.) 6 ft.

2.) h = 1820 meters.

Reference Book:Geometry textbook for third yearAuthor-EditorSOLEDAD JOSE DILAOJULIETA BERNABEWEBSITE:http://www.analyzemath.com/Geometry/similar_triangle_problems.html

http://www.mathopenref.com/similartriangles.html

Consider the following figures: B Y

A C X Z We say that ABC ~ XYZ if and only ifAngles A is congruent to angle X , angle B is congruent to angle Y , angle C is congruent to angle Z .

exampleGiven that ABC ~ DEF. find the values of x and y.

B E

3 4 X 8 A C D F

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Solution Since the corresponding sides are proportional, we have . AB BC AC DE EF DF3 4 5X 8 y

3 1 5X 2 y x=6;y =10more information at yourteacher.com Activity:# 22. 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. #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. Assessment .#2

Reference Friends: Rovan EscamaCarlo Jan bajalanJerome CapellanFamily:Mother &father

THANKS FOR WATCHINGPrepared BY:MEYNARD MACABENTA

Solution no.#1 activity cardWe now use the proportionality of the lengths of the side to write equations that help in solving for x and y.

(30 + x) / 30 = 22 / 14 = (y + 15) / yAn equation in x may be written as follows.

(30 + x) / 30 = 22 / 14Solve the above for x.

420 + 14 x = 660

x = 17.1 (rounded to one decimal place).An equation in y may be written as follows.

22 / 14 = (y + 15) / ySolve the above for y to obtain.

y = 26.25