Similar triangles ?

Similar triangles ?

Similar Triangle go

DRILL • MOTIVATION • SIMILAR TRIANGLES • VIDEO OF SIMILAR TRIANGLES • Activity card • Assessment card • Answer key • Reference Guideline:

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. Drill or pre-test

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

1. A.29.25 B.25.26 C.26.25 D.23.24 2.A.H= 60 B. H= 30 C. H= 56 D. H= 10 Choose wisely

My motivation 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,

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. Similar triangles

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 .

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

Since the corresponding sides are proportional, we have . AB BC AC DE EF DF 3 4 5 X 8 y 3 1 5 X 2 y x=6;y =10 Solution

more information at “yourteacher.com”

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

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. Activity:# 2

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 no.#1

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

Assessment .#2

ACTIVITY CARD • ASSESMENT CARD • 1.) 6 ft. • 2.) h = 1820 meters. Answer keys

Book: Geometry textbook for third year Author-Editor SOLEDAD JOSE DILAO JULIETA BERNABE • WEBSITE: http://www.analyzemath.com/Geometry/similar_triangle_problems.html http://www.mathopenref.com/similartriangles.html Reference

Friends: • Rovan Escama • Carlo Jan bajalan • Jerome Capellan • Family: • Mother &father Reference

THANKS FOR WATCHING Prepared BY:MEYNARD MACABENTA

We 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) / y • An equation in x may be written as follows. (30 + x) / 30 = 22 / 14 • Solve 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) / y • Solve the above for y to obtain. y = 26.25 Solution no.#1 activity card

Solution to Problem 2: • We first draw a horizontal line LM. PP' and MM' are vertical to the ground and therefore parallel to each other. Since PP' and MM' are parallel, the triangles LPP' and LMM' are similar. Hence the proportionality of the sides gives: 1010 / 10 = (h - 2) / 18 • Solve for h to obtain h = 1820 meters. Solution no.#2 activity card

Your correct SEE SOLUTION

Not correct

Similar triangles ?