Download Unit 5 Test Honors - Rancho High School

Unit 5H Test
Name________________________Period_______
Read all of the questions carefully. All work must be shown under the appropriate problem
to receive full credit. Label all diagrams and proofs appropriately. (2 points each unless
specified) 60 pts total.
1ABC and DEF have the following properties:
,
and
. Drawing is NTS.
B
E
A
If
m
a.
b.
C
F
D
= 15,
= 14, and m
= 30 , and
= (5n + 15)°, determine the value of n.
11
n=2
c.
n= 3
n=3
d.
n=9
2. In the triangles shown below,
may be combined to map
onto
listed in order. Circle all that apply.
,
y
A
X
B
C
Y
x
Z
a.
b.
c.
d.
e.
A reflection across the x-axis
A reflection across the y-axis
A reflection across the line
A vertical translation
A horizontal translation
= n + 12,
= 3n + 5, and
, and
. Which rigid motions below
? This requires a composition of transformations. They are
For questions 3-4, consider ABC where AB = BC and mA  40 .
3. mB  mC  140
(A) True
(B) False
4. mC  100
(C) True
(D) False
5. Given:
;
and
are right angles.
Prove:
Proof:
Which justification belongs in Step 2?
a.
Isosceles Theorem
b.
Reflexive Property of Congruence
c.
Right Angles are Congruent Theorem
d.
CPCTC
6. In the figure, H is the midpoint of
(A)
(B)
and
SAS
ASA
. What reason can be used in a proof to show
(C) Def. of bisector
(D) CPCTC
?
7.
and
are altitudes to the congruent sides of isosceles triangle
.
W
Q
P
X
Y
Keisha is going to prove
by showing they are congruent parts of the congruent triangles
and
.
By what congruence postulate is
?
a.
AAS - because triangle WXY is isosceles, its base angles are congruent. Perpendicular lines form
right angles, which are congruent; and segment
is shared.
b.
SSS - because segment
would be parallel to segment
.
c.
SSA - because segment
is shared; segments
and
are altitudes, and WXY is isosceles,
so base angles are congruent.
d.
ASA - because triangle WXY is isosceles, its base angles are congruent. Segment
is shared;
and perpendicular lines form right angles, which are congruent.
8. Which of the following statements can be concluded from the given triangle?
S
U
a.
b.
c.
d.
e.
f.
g.
h.
T
is an isosceles triangle.
is an equilateral triangle.
9. Given:
ASA.
10.
,
. State the congruence that is needed to prove
using
Which figure contains two triangles that are NOT congruent?
a.
c.
d.
b.
For questions 11-13, consider a triangle ABC that has been transformed through rigid motions
and its image compared to XYZ . Determine if the given information is sufficient to draw the
provided conclusion.
11.
e. Given
A  X
B  Y
C  Z
(A) True
(B) False
Conclusion
ABC  XYZ
Given
A  X
B  Y
12.
Conclusion
ABC  XYZ
BC  YZ
(A) True
(B) False
13.
Given
A   X
Conclusion
AB  XY
ABC  XYZ
BC  YZ
(A) True
(B) False
14. Use the triangle. What is the value of x?
80 °
(A) 75
(B) 25
x°
 4 x  25  
(C) 21
(D) 15
15. In the isosceles triangle below, mH  124 . What is the measure of F ?
(A) 28°
H
(B) 56°
124°
(C) 124°
(D) 180°
G
F
16. What term describes a transformation that does not change a figure’s size or shape?
(A) Reflexive
(C) Conguent
(B) Dilation
(D) Isometry
17.
Find the coordinates of the other endpoint of the segment with the given endpoint A and
midpoint M. 𝐴(−4, 3) and 𝑀(−2, −1)
______________
18.
Given A  2,  6  and B  4,  2  . What is the distance from A to B?
______________
19. In the diagram, mABC  85 . What is the value of x? Grid your answer in the box.
A
 3 x  10 
B
D
 2x  
C
20. Given that ∠1 ≅ ∠3, which lines must be parallel?
21. (3 points) Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which
congruence postulate or theorem you would use and mark it correctly on the diagram.
22.
and
are congruent.
y
5
L
4
3
2
K
1
J
–5
–4
–3
–2
–1
–1
1
O
2
3
4
5
x
–2
–3
N
–4
M
–5
Use correct mathematical notation to explain what transformation or transformations would map
to
23. Which lines, if any, must be parallel based on the given diagram and information and WHY. Given
𝑚∠8 = 𝑚∠13.
a
1
2
9 10
3 4
b
11
5
6
7
8
c
24. (4 points) Solve the equation and state a reason for each step:
2(𝑥 − 1) + 3 = 17
12
13 14
15 16
d
?
25. In the diagram, NK  LM and 1  2 . Prove LMK  NKM . (3 points)
L
1
K
⃡ is the perpendicular bisector of AB . (6 points)
26. In the diagram, 𝐷𝐶
D
A
C
B
Prove ̅̅̅̅
𝐷𝐴 ≅ ̅̅̅̅
𝐷𝐵.
N
2
M