Honors Geometry 3. Homework Answers for Section 8.3 Given: NPVR is a parallelogram
N
O
P
W
Prove:
NWO ∼
SWT
R
T
Statements
1. NPVR is a !
A 2. ∠NWO ≅ ∠SWT
3. NP
RV
A 4. ∠NOW ≅ ∠STW
5. NWO ∼ SWT
S
V
Reasons
1. Given
2. VAT
3. Definition of !
4. PAI
5. AA ∼ (2, 4)
4. A
Given: AC ≅ AE
∠CBD ≅ ∠EFD
B
F
Prove:
BCD ∼
FED
C
Statements
1. AC ≅ AE
A 2. ∠C ≅ ∠E
A 3. ∠CBD ≅ ∠EFD
4. BCD ∼ FED
Baroody D
E
Reasons
1.
2.
3.
4.
Given
ITT
Given
AA ∼ (2, 3)
Page 1 of 3 Honors Geometry 12. Given:
Prove:
Homework Answers for Section 8.3 N
SP is the altitude from S to NR
RT is the altitude from R to NS
NRT ∼
P
T
NSP
S
R
Statements
Reasons
1. SP is the altitude from S to NR
1. Given
2. SP ⊥ NR
3. ∠SPN is right
2. Definition of Altitude
3. Definition of ⊥ Segments
4. RT is the altitude from R to NS
4. Given
5. RT ⊥ NS
5.
6.
7.
8.
9.
6. ∠RTS is right
A 7. ∠SPN ≅ ∠RTN
A 8. ∠N ≅ ∠N
9. NRT ∼ NSP
Definition of Altitude
Definition of ⊥ Segments
RAT
Reflexive Property
AA ∼ (7, 8)
16. Indicate whether the statement is true Always, Sometimes, or Never (A, S, or N)
a. If two triangles are similar, then they are congruent.
S
b. If two triangles are congruent, then they are similar.
A
c. An obtuse triangle is similar to an acute triangle.
N
d. Two right triangles are similar.
S
e. Two equilateral polygons are similar.
S
f. Two equilateral triangles are similar.
A
g. Two rectangles are similar if neither is a square.
S
Baroody Page 2 of 3 Honors Geometry 19. Homework Answers for Section 8.3 Given: Figure as shown
Does
a. Is PQT ∼ PRS? Justify
your reasoning.
QP
RP
4
10
b. Is QT parallel to RS? Justify
your reasoning.
=
=
TP
SP
6
15
?
=
2
5
, so the sides are proportional
∠P is in both triangles, so
PQT ∼
PRS by SAS ∼
Since the triangles are similar, all the angles are congruent.
∴ ∠PQT ≅ ∠R.
R
QT
6
RS by CAP
Q
4
P
T
6
S
9
22. If two of the six triangles below are selected at random, what is the probability that the two triangles
are similar?
50°
30°
100°
50°
100°
30°
80°
80°
60°
60°
1st Pick
30, 50, 100
40, 60, 80
Baroody 60°
40°
2nd Pick
3
6
•
2
6
•
2
5
=
1
5
=
2
10
1
15
8
4
=
30
15
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