Download Name: Date: ______ Day 15: Proofs Quiz Geometry CC (M1L9) Part

Name: ____________________________________________________________________ Date: __________
Day 15: Proofs Quiz
Geometry CC (M1L9)
Part I – Each question is worth 2 points.
Refer to the figure and choose the best answer for #1 and #2.
R
1. Which could be used to find the value of x?
a. Subtraction Postulate
b. Definition of Complementary Angles
c. Substitution
d. Definition of supplementary Angles
S
x-1
2. What is the m<SQR?
2x+ 4
P
Q
3. Use the diagram, which statement would be used to prove lines r and s are parallel?
a. <1 and <3 are supplementary
b. <4 and <8 are corresponding
c. <4 and <1 are vertical
d. <8 and <6 are corresponding
s
r
1
2
4
3
m
n
8
7
6
5
4. In the diagram, BD intersects AE at C. Which of the following conclusions does not have to be true?
a.
b.
c.
d.
<ACB ≅ <ECD
<ACB ≅ <ACD form a linear pair
<BCE and <ACD are vertical angles
<BCE and <ECD are corresponding angles
E
B
C
A
5. Angle X and angle Y are both supplementary and congruent. This means they must be
a.
b.
c.
d.
Vertical angles.
Acute angles.
Right angles.
Complementary Angles.
D
Part II – Answer all questions. Point value assigned to each question
5. Prove that if DB bisects <ADC, then <2 ≅ <3. ( each reason is worth 2 points)
Given: DB bisects <ADC
Statements
Reasons
Prove: <2 ≅ <3
1.
DB bisects <ADC
1.
B
A
2. < 1 ≅ < 2
2.
1.
<1 ≅ <3
3.
2.
<2 ≅ <3
4.
C
1
2
D
3
1
4
6. Given: p
2
p
3
q
Prove: m<3 = m<5
5 6
Complete the proof by writing the missing statements and reasons.
(1 point each fill-in)
STATEMENTS
8
7
q
REASONS
1)
1)
2) m<3 + m<6 = 180°
2)
3)
3)
4) m<3 + m<6 = m<5 + m<6
4)
5) m<3 = m<5
5)
Given
Linear pairs of angles are supplementary
7. In the diagram at the right, prove that the sum of the labeled angles is 180°.
x
z
8. In the figure at the right, 𝐴𝐵  𝐶𝐷 and 𝐵𝐶  𝐷𝐸.
Prove that m𝑨𝑩𝑪 = m𝑪𝑫𝑬.
y
9. Given: Triangle ABC
Prove: m<ACD = <1 + <2
D
10. Prove line l is parallel to line m