8.5 Proving Triangles are Similar

Objectives:Use similarity theorems to prove that 2 triangles are similarUse similar triangles to solve real problems

SSS Similarity Theorem

If the lengths of the corresponding sides of 2 triangles are proportional, then the triangles are similar.

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.

Which of these are similar?

12

69 8

64

106

14

Match the sides . . .

12

69 8

64

106

14

Purple Blue Orange

Shortest Side: 4 6 6

Middle Side: 6 9 10

Longest Side: 8 12 10

Do the ratios

12

69 8

64

106

14

Purple Blue Orange P/B B/O

Shortest Side: 4 6 6 4:6 6:6

Middle Side: 6 9 10 6:9 9:10

Longest Side: 8 12 10 8:12 12:10

Reduce the ratios . . .

12

69 8

64

106

14

Purple Blue Orange P/B B/O

Shortest Side: 4 6 6 4:6 2:3 6:6 1:1

Middle Side: 6 9 10 6:9 2:3 9:10 9:10

Longest Side: 8 12 14 8:12 2:3 12:14 6:7

Using a Pantograph

A pantograph is a mechanical device that draws an enlargement:

PantographEnlargements are similar to the original.http://www.ies.co.jp/math/java/geo/panta/

panta.html

Finding Distance Indirectly

Look at the picture on p. 491. The person’s eyes are 5 feet from the ground. The angle from the person to the mirror is the same as

from the mirror to the top of the wall. The person is 6.5 feet from the mirror. The mirror is 85 feet from the wall. Height = 85 5 6.5 When solving problems like this, DRAW PICTURES!!!

Homework

Do worksheets