Download 6.2 and 6.3 Notes

DMR #4

Homework Answers
1. 1in : 278 in
16. 12
17. 12
19. 4.2
20. 8
22. 6
23. 2.5
18. 33
21. 29.3
24. -2.5
Unit 6
6.2 Similar Polygons
Definitions
Two polygons are _______________ if:
(1) Corresponding angles are congruent
(2) Corresponding sides are proportional
*figures have the same shape but not
necessarily the same size.
The ratio of the lengths of corresponding
sides is the ______________ _________.
Example 1

The figures are similar. Complete each
statement.
B
C
F
A
G
127о
53о
(a) m‫ے‬E =
D
E
(b) AB
EF
Try
(a) m‫ے‬B =

AD
(b) GH  FG
CD
H
Example 2
Determine whether the triangles are
similar. If they are, write a similarity
statement and give the similarity ratio.
15
12
18
16
20
24
Try
Sketch two triangles with congruent
corresponding angles. The first triangle
has sides 12, 14, and 16. The second has
sides 18, 21, and 24. Are the triangles
similar? If so, give the similarity ratio.
Example 3
The figures are similar. Find x.
6
5
y
3.2
2
Try: Find y.
x
Challenge!!
A video projector magnifies images. If the
projector’s screen is 16 in wide x 12 in tall,
what is the largest complete image
possible for an image that is 6 in wide x 4
in tall?
Homework
#1-16
DMR #5

Homework Answers
1. Yes, ΔABC ~ ΔXYZ, 2/1
2. Yes, ΔQMN ~ ΔRST, 5/3
3. No, angles not congruent
4. No, angles not congruent
5. Yes, ΔABC ~ ΔKMN, 4/7
6. No, 9/6 ≠ 4/4
7. ‫ے‬I
8. ‫ے‬O
10. NO
11. LO
13. 3.96
14. 4.8
15. 3.75
16. 10
9. ‫ے‬J
12. LO
Unit 6
6.3 Proving Triangles Similar
Day 1
Angle-Angle-Similarity (AA~)
If two angles of one triangle are congruent
to two angles of another triangle, then the
triangles are similar
M
ΔTRS ~ ΔPLM
S
T
L
R
P
Example 1
MX ┴ AB. Are the triangles similar? If so,
state the reason and write a similarity
M
statement.
K
A
58
58 B
X
Try
Are the triangles similar? If so, state the
reason and write a similarity statement.
W
V
45
S
45
R
B
Side-Angle-Side Similarity (SAS~)
If an angle of one triangle is congruent to
an angle of a second triangle, and the
sides including the two angles are
proportional, then the triangles are similar.
M
S
ΔTRS ~ ΔPLM
6
3
L
T
4
R
P
8
Example 2
Are the triangles similar? If so, state the
reason and write a similarity statement.
W
Z
24
18
V
12
Y
36
X
Try
Are the triangles similar? If so, state the
reason and write a similarity statement.
K
2 70◦
J
3
N
4
70◦
M
6
P
L
Side-Side-Side Similarity (SSS~)
If the corresponding sides of two triangles
are proportional, then the triangles are
similar.
ΔTRS ~ ΔPLM
M
S
3.5
6
7
3
L
T
4
R
P
8
Example 3
Are the triangles similar? If so, state the
reason and write a similarity statement.
12
E
G
B
6
6
8
8
C
A
9
F
Try
Are the triangles similar? If so, state the
reason and write a similarity statement.
I
E
S
Q
O
U
Challenge!!
Are the triangles similar? If so, state the
reason and write a similarity statement.
Y
C
X
A
30◦
12
B
8
30◦
Z
Homework
#1-6
DMR #6

Homework Answers
1. ΔABX ~ ΔRQX by AA~
2. ΔMPX ~ ΔLWA by SAS~ or SSS~
3. ΔQMP ~ ΔAMB by SAS~
4. ΔMJN ~ ΔACB by AA~
5. ΔABX ~ ΔCRX by SAS~
6. ΔABC ~ ΔXYZ by SSS~
Unit 6
6.3 Proving Triangles Similar
Day 2
Example 1
The triangles are similar. Find x.
10
12
24
16
18
x
Try
The triangles are similar. Find x.
12
x
6
8
Example 2
The triangles are similar. Find x.
6
9
4
21
x
6
Example 2
The triangles are similar. Find x.
8
10
12
33
x
15
Example 3
In sunlight, a cactus casts a 9-ft shadow.
At the same time a person 6-ft tall casts a
4-ft shadow. Use similar triangles to find
the height of the cactus.
Try
Beth places a mirror on the ground 8ft
from the base of an oak tree. She walks
backward until she can see the top of the
tree in the mirror. At that point, Beth’s
eyes are 5ft above the ground, and her
feet are 3ft from the image in the mirror.
Find the height of the oak tree.
Challenge!!
The triangles are similar. Find x.
8
6
x
16
Homework: #7-13