Transcript Proving Triangles Similar

C
Check for Understanding – p. 256 #1-11
DABC ~ DDEF. True or False?
1. DBAC ~ DEFD
False
A
B
2. If mD = 45, then mA = 45 True
3. If mB = 70, then mF = 70 False
4.
AB EF

DE BC
F
False
D
E
F
Check for Understanding – p. 256 #1-11
DABC ~ DDEF. True or False?
AC AB
True

5.
DF DE
D
6. If DF:AC = 8:5, then mD:mA = 8:5 False
C
7. If DF:AC = 8:5, then EF:BC = 8:5 True
E
A
B
8. If the scale factor of DABC to DDEF is 5 to 8,
then the scale factor of DDEF to DABC is 8 to 5.
True
We could prove that two triangles are
similar by verifying that the triangles
satisfy the two pieces of the definition
of similar polygons
1. the corresponding angles are
congruent, and
2. The corresponding sides follow the
same scale factor throughout the figure.
However, when dealing with triangles,
specifically, there are simpler methods.
Postulate 15 – AA Similarity Postulate
If two angles of one triangle are
congruent to two angles of another
triangle, then the two triangles are
similar.
Ex. If A @ D and B @ E,
E
then DABC ~ DDEF
B
A
C
D
F
Check for Understanding – p. 256 #1-11
9. One right triangle has an angle with
measure 37. Another right triangle has
an angle with measure 53. Are the two
triangles similar? Explain.
Yes, AA Similarity Postulate.
53°
53°
37°
37°
Theorem 7-1 SAS Similarity Theorem
If an angle of one triangle is congruent to
an angle of another triangle and the sides
including those angles are in proportion,
then the triangles are similar.
If: A @ D
AB AC

DE DF
E
B
C
A
Then: DABC ~ DDEF
D
F
Theorem 7-2 SSS Similarity Theorem
If the sides of two triangles are in
proportion, then the triangles are similar.
B
E
A
If:
AB BC AC


DE EF DF
C
Then: DABC ~ DDEF
D
F
Check for Understanding p. 264-5 #1-6
Can the two triangles shown be proved similar? If so, state
the similarity and tell which postulate or theorem is used.
1.
R
2. C
24
16
X
F
10
H
16 8

10 5
S
32
20
15
E
70
40
G
24 8 32 8


15 5 20 5
SSS Similarity Thm.
DHFG ~ DRXS
J
Not Similar
N
D
60
70
U
Check for Understanding p. 264-5 #1-6
Can the two triangles shown be proved similar? If so, state
the similarity and tell which postulate or theorem is used.
3.
4. W
T
6
12
12
R
S
8
X
9
U
Y
V
8
Q
9
6
12 4

9 3
8 4

6 3
SAS Similarity Theorem
No Conclusion
DRQS ~ DUTS
Z
Check for Understanding p. 264-5 #1-6
Can the two triangles shown be proved similar? If so, state
the similarity and tell which postulate or theorem is used.
5.
L
A
9
15
P
25
15 3

25 5
N 9
L
A
9 3

15 5
15 N
L
15
P
25
N
DLNP ~ DANL SAS Similarity Thm.
Check for Understanding p. 264-5 #1-6
Can the two triangles shown be proved similar? If so, state
the similarity and tell which postulate or theorem is used.
A
6.
A
21
30
24
30
D
24
16
C
B
B
36
C
36
24 3

16 2
30 10

21
7
36 3

24 2
D
16
C
24
21
A
These Triangles are NOT Similar!
Problem Solving
x
1.5m
3m
8m
3 1 .5

8 x
3x = 12; x = 4
Linda wants to determine the height of this
tree. She measured the shadow of the tree as
8m and her own shadow was 3m. She knows
that she is 1.5m tall. How tall is the tree? 4m