Download 8.3 Proving Triangles Similar

Warm up…
• checkpoint quiz page 429 #’s 1 – 10
8.3 Proving Triangles Similar
SWBAT…
• To use AA, SAS, and SSS similarity
statements
• To apply AA, SAS and SSS similarity
statements.
Investigation: triangles w/ 2 pairs of
congruent angles
• Use page 432 and complete the
investigation in the blue box.
• We’ll have a class discussion in 4 minutes.
Angle – Angle Similarity (AA~)
Postulate
• If two angles of one triangle are congruent
to two angles of another triangle, then the
triangles are similar.
S
B
R
T
A
C
If angles A and R are congruent and angles B and S are
congruent (mark them), Then triangle ABC ~ triangle RST
Example 1
• MX is perpendicular to AB. Explain why
the triangles are similar. Write a similarity
statement.
M
K
B

58

58
X
A
Side Side Side Similarity
• THEOREM: if the corresponding sides of
two triangles are proportional, then the
triangles are similar.
S
B
R
T
A
C
Example 2
• If AB = 18, BC = 12, AC = 21, RS = 6, ST
= 4, RT = 7 are the triangles similar?
S
B
R
T
A
C
Side – Angle – Side (SAS ~)
• If the measures of two sides are
proportional to the measures of two
corresponding sides of another triangle
and the included angles are congruent,
then the triangles are similar.
S
B
R
A
C
T
Example 3
S
B
12
6
8
R
A
C
Are the two triangles similar?
4
T
Example 4
• In the figure AB || DC,
CD  DE , AB  BE , BE  27,
DE  45, AE  21, CE  35
Determine which triangles are similar.
C
B
E
A
D
Example 5
• Given UT || RS, find SQ and QU.
U
R
2x + 10
10
4
X+3
S
T
Example 6
• If you wanted to
measure the height of
the Sears tower in
Chicago, you could
measure a 12-foot light
pole and measure its
shadow. If the length of
the shadow was 2 feet
and the shadow of the
Sears Tower was 242
feet, what is the height of
the Sears Tower?
Class work…
• Page 435 – 436 #’s 1 – 19, 23, 45 – 48
• We do have a short quiz Monday on what
we’ve covered in Ch. 8
• Chapter 8 test is Friday of next week.