Download Before: October 18, 2013

Before: March 30, 2016
During: Proving Triangles
Similar
OBJECTIVE: TO USE THE AA ~ POSTULATE
AND THE SAS ~ AND SS ~ THEOREMS. TO
USE SIMILARITY TO FIND INDIRECT
MEASUREMENTS.
Postulate 7 – 1
 You can show that two triangles are similar when
you know the relationships between only two or
three pairs of corresponding parts.
Angle-Angle Similarity (AA ~) Postulate
Postulate
If two angles of one
triangle are
congruent to two
angles of another
triangle, then the
triangles are
similar.
If…
Then…
Problem 1: Using the AA ~ Postulate “I Do”
 Are the two triangles similar? How do you know?
A. Triangle RSW and Triangle VSB
B. Triangle JKL and Triangle PQR
Problem 1: Using the AA ~ Postulate “We Do”
 Are the two triangles similar? How do you know?
Problem 1: Using the AA ~ Postulate “You Do”
 Are the two triangles similar? How do you know?
Theorem 7 – 1 and Theorem 7 - 2
Side – Angle – Side Similarity (SAS ~ ) Theorem
Theorem
If…
Then…
If an angle of one triangle
is congruent to an angle
of a second triangle, and
the sides that include the
two angles are
proportional, then the
triangles are similar.
Side – Side – Side Similarity (SSS ~ ) Theorem
Theorem
If the corresponding sides
of two triangles are
proportional, then the
triangles are similar.
If…
Then…
Problem 2: Verifying Triangle Similarity “I Do”
 Are the triangles similar? If so, write a similarity
statement for the triangles.
Problem 2: Verifying Triangle Similarity “We Do”
 Are the triangles similar? If so, write a similarity
statement for the triangles.
Problem 2: Verifying Triangle Similarity “You Do”
 Are the triangles similar? If so, write a similarity
statement for the triangles.
Sometimes you can use similar triangles to find
lengths that cannot be measured easily.
 You can use indirect measurement to find
lengths that are difficult to measure directly.
 One method of indirect measurement uses the fact
that light reflects off a mirror at the same angle at
which it hits the mirror.
Problem 4: Finding Lengths in Similar Triangles
“I Do”
 Before rock climbing, Darius wants to know how
high he will climb. He places a mirror on the ground
and walks backward until he can see the top of the
cliff in the mirror. What is the height of the cliff?
Problem 4: Finding Lengths in Similar Triangles
“We Do”
 Benjamin places a mirror 40 ft from the base of an
oak tree. When he stands at a distance of 5 ft. from
the mirror, he can see the top of the tree in the
reflection. If Benjamin is 5 ft. 8 in. tall, what is the
height of the oak tree?
After: Lesson Check
 Are the triangles similar? If yes, write a similarity
statement and explain how you know they are
similar.
Are the Triangles Similar?
Activity
OBJECTIVE: PROVE THAT 2
TRIANGLES ARE SIMILAR USING
AA~, SAS~, AND SSS~.
Homework:
PAGE 455, #8 – 12, 15, AND 16