Download Chapter 4 Review HW KEY

Geometry
Chapter 4 Review
Name:_________________________________
1. What are the lengths of the sides of this equilateral triangle?
2. How would △ABC with vertices A(4, 1), B(2, –1), and C(–2, 1) be classified based on the length of its sides? You must
verify with work.
Use the figure for Questions 3 – 5.
3. What is m∠1?
4. What is m∠2?
5. What is m∠3?
���� ?
6. If △DJL ≅ △EGS, which segment in △EGS corresponds to 𝐷𝐿
7. Which triangles are congruent in the figure?
A) △KLJ ≅ △MNL
B) △JLK ≅ △NLM
C) △JKL ≅ △LMN
D) △JKL ≅ △MNL
8. Given that ∆KML ≅ ∆CBA, find the value of x.
9. Quadrilateral MNQP is made of two congruent triangles.
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𝑁𝐴 bisects ∠N and ∠P. In the quadrilateral, m∠N = 50
and m∠P = 100. What is the measure of ∠M?
10. Find the value of x.
11. Which of the following is a correct congruence statement for the triangles shown?
a) ∆ABD ≅ ∆BCD
b) ∆ADB ≅ ∆BCD
c) ∆DAB ≅ ∆BCD
d) the triangles cannot be proven they are congruent
e) none of the above
Decide whether it is possible to prove that the triangles are congruent. If it is possible, name the correct reason. If it is not possible to
prove the triangles are congruent with the given information, say “not possible.”
12.
L
13.
P
14.
O
15.
U
Y
R
W
K
N
M
T
V
X
S
16. What are the missing coordinates of the triangle?
17. Find the value of x.
4x + 10
18. Find the value of x.
19. Find the measures of angle 1 and 2.
70°
28◦
3x + 5
(3x – 10)°
62◦
2
5x - 25
1
20. △ABC is located in the coordinate plane with A(0, 0), B(b, 0) and C(a, c). Find the coordinates of M the midpoint of
AC and N the midpoints of BC .
For numbers 21 – 23, complete each proof. Use the reasons word bank for help (located on back page). Choose one method to write
the proofs (flow or two-column).
21. Given: ∠𝐴𝐴𝐴 ≅ ∠𝐷𝐴𝐴
���� bisects ∠𝐴𝐴𝐷
𝐴𝐴
Prove: ∆AFP ≅ ∆DFP
A
F
D
Statements
Reasons
1.
2.
∠𝐴𝐴𝐴 ≅ ∠𝐷𝐷𝐷
1.
2. Given
3.
3. Definition of Bisects
4.
4.
5.
5.
P
∠𝐴𝐴𝐴 ≅ ∠𝐷𝐴𝐴
_______________________
Given
Definition of Bisects
_____________________
_________________________
22. Given: AB ≅ DB
AC ≅ DC
Prove: ∡A ≅ ∡D
A
Statements
Reasons
1.
1.
2.
2
3.
3.
4. ∆BAC ≅ ∆________
4.
5.
B
D
5.
_______________________
____________________
_________________________
∆BAC ≅ ∆________
___________________
C
_____________________
����� and ����
23. Given: N is the midpoint of 𝑀𝐴
𝑄𝑂
Prove: ∆MNQ ≅ ∆PNO
Statements
Reasons
1.
1. Given
2.
2. Midpoint Theorem
3. N is the midpoint of ����
𝑄𝑂
3.
���� ≅ ����
4. 𝑄𝑁
𝑂𝑁
4.
5. ∠MNQ ≅ ∠PNO
5.
6.
6.
����
N is the midpoint of 𝑄𝑂
_______________________________
Reasons Word Bank
Definition of Congruent Angles
Definition of Congruent Segments
Reflexive Property
Symmetric Property
Transitive Property
Given
Midpoint Thm.
Definition of Bisects
Definition of Perpendicular
If parallel lines, then alt. int.
angles congruent
Vertical Angles are congruent
SSS
SAS
ASA
AAS
HL
CPCTC
����
𝑄𝑁 ≅ ����
𝑂𝑁
_____________________
∠MNQ ≅ ∠PNO
_____________________
Given
______________
Midpoint Theorem