Download Notes for Lesson 7.4

Postulate &
Theorems for Similar
Triangles
Unit 6: Lesson 7.4-7.5
Postulate 15 AA Similarity Postulate : If two angles of one triangle are
congruent to two angles of another triangle, then the triangles are similar
Example 1: Tell whether the triangles are similar or not similar
a.
b.
Similar
Similar
c.
d.
Similar
Similar
Practice p257 written exercises #1-9 odd
Example 2: Find the value of x
a.
5
3
1
X = 5/3
x
A
△EBD
b. △ABC ∼ ______
32/7
c. y = ______
BD
BE
9/4
d.
 _____,
BC so x  ______
BA
x
8
E
y
C
Practice p257 written exercises 10 and 12
3
D
3
4
B
Theorem 7-1
SAS Similarity Thm : If an angle of one triangle is congruent to the angle of
another triangle and the sides including those angles are in proportion, then the
triangles are similar
Theorem 7-2
SSS Similarity Thm: If the sides of two triangles are in proportion, then the
triangles are similar
Example 3: Name similar triangles and give the postulate or theorem that
justifies your answer.
a.
b.
A
B
D 80°
80°
E
△ADE∼△ABC
AA ∼ Post.
C
c.
C
6
D
3
A
10
△CDE∼△CAB
SAS ∼ Thm
E
L
3
K
5
B
6
5
6
M 6
10
O
△KLM∼△KON
SSS ∼ Thm
N
Practice p264 Classroom Exercises #1-4
Example 4: If △ABC ∼△DEF, does AB correspond to DE ?
Does BC correspond to EF ?
Yes
Does AC correspond to DF ?
Yes
Yes
Practice
1. The measures of the sides of △ABC are 4, 5, and 7, and the measures of
the sides of △XYZ are 16, 20, and 28. Are the two triangles similar?
Yes
1. In △ABC , AB = 2, AC = 5, and BC = 6. In △XYZ , XY = 2.5, YZ = 2, and
XZ = 3. Is △ABC ∼ △XYZ ?
No
Homework: Practice Worksheet 7.4 and 7.5