7.3 Proving Triangles Similar

-AA Similarity -SSS Similarity -SAS Similarity

• We can prove that 2 triangles are similar by showing that all 3 corresponding angles are congruent, and all 3 sides are in proportion to one another (same as showing any 2 polygons similar) • But there are simpler methods to prove 2 triangles similar.

AA Similarity Postulate

• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Are these triangles similar, if so, then why? Can you find x? And AE and ED? What is the scale factor?

SAS Similarity Theorem

• If an angle of one triangle is congruent to an angle in another triangle and the sides including those angles are in proportion, then the triangles are similar.

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

• Use the given lengths to prove that

∆RST

~

∆PSQ.

4

P S

5

Q

Given: SP=4, PR = 12, SQ = 5, and QT = 15; Prove: ∆RST

~

∆PSQ

12 15

R T

SSS Similarity

• If all the sides of two triangles are in proportion, then the triangles are similar.

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

What do x and y have to be in order for these 2 triangles to be similar by SSS?

A B x 6 E y C 15.2

D

What similarity do these 2 triangles have?

• A very common class of exercises is finding the height of something very tall by using the daytime shadow length of that same thing, its shadow being down along the ground, and thus easily accessible and measurable. You use the known height of something shorter, along with the length of its daytime shadow as measured at the same time.

•

A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow. How tall is the building? (Round your answer to the nearest tenth.)

• Nate and Sam are visiting Washington D.C. They want to know the height of the Washington Monument. The monument’s shadow is 111 feet at the same time that Sam’s shadow is 1 foot. Sam is 5 feet tall.