Name: _____________________________________
Homework 1: Complementary and Supplementary Angles
Homework 2: More Complementary and Supplementary Angles
Homework 3: Parallel Lines
Homework 4: Proving Lines Parallel
Homework 5: More Parallel Line Proofs
Homework 6: Perpendicular Line Proofs
Homework 7: More Perpendicular Line Proofs
Homework 8: Mixed Practice
Date: ___________
Homework 1: Complementary and Supplementary Angles
1. Two complementary angles are in the ratio of 7:8. Find the measure of each angle.
̅̅̅̅, 𝑚∠𝑄𝑅𝑆 = 3𝑥 + 4, and
2. Given the diagram to the right, ̅̅̅̅
𝑄𝑅 ⊥ 𝑅𝑇
𝑚∠𝑆𝑅𝑇 = 6𝑥 − 22, find 𝑚∠𝑆𝑅𝑇.
Q
S
T
R
3. Determine the value of the supplement of the given angles:
a.) 𝑚∠𝐴 = 36
b.) 𝑚∠𝐵 = 12
c.) 𝑚∠𝐶 = 4x
d.) 𝑚∠𝐷 = x + 5
4. Determine the value of the complement of the given angles:
a.) 𝑚∠𝐸 =59
b.) 𝑚∠𝐹 = 11
c.) 𝑚∠𝐺 = 3x
d.) 𝑚∠𝐻 = 2x – 6
For problems 5 – 7,
5.
6.
7. If 𝑚∠𝐵𝐸𝐶 = 5𝑥 − 25 and 𝑚∠𝐴𝐸𝐶 = 4𝑥 + 25, find 𝑚∠𝐵𝐸𝐶, 𝑚∠𝐴𝐸𝐶, 𝑚∠𝐴𝐷𝐸, and 𝑚∠𝐷𝐸𝐵.
Statements
Reasons
8. Prove the theorem that
we discussed in class:
1. ABC is a right angle
1. Given
“If two adjacent angles form a right angle,
2.
2.
3. m1  m2  mABC
3. Partition
then they are complementary”
A
(the whole is = to the
sum of its parts)
1
2
B
9.
C
4. 𝑚∠1 + 𝑚∠2 = 90°
4.
5.
5. If two angles have a
sum of 90°, then they are
complementary
Given: 2  4
Prove: 1  3
5.
and
are
complementary
2
4
1
3
5.
Homework 2: More Complementary and Supplementary Angles
1. In the diagram to the right, 𝑚∠𝐴𝐵𝐷 = 2𝑥 + 22 and 𝑚∠𝐷𝐵𝐶 = 2𝑥 + 122.
Find the measure of ∠𝐷𝐵𝐶
A
D
B
C
For problems 2 – 4, write the final theorem that you would use to prove the given statement.
2. ∠1 and ∠2 are supplementary and m∠2 + m∠3 = 180. Prove that m∠1 = m∠3.
3. ∠𝐴 and ∠𝐵 are adjacent angles that form a right angle, 𝑚∠𝐶 + 𝑚∠𝐷 = 90, and ∠𝐴 ≅ ∠𝐷.
Prove that ∠𝐵 ≅ ∠𝐶.
4. ∠𝑆 and ∠𝑇 form linear pair, ∠𝑅 and ∠𝑄 form linear pair and ∠𝑇 ≅ ∠𝑄. Prove that ∠𝑆 ≅
∠𝑅.
5. Given: ∠1 ≅ ∠4
Prove: ∠2 ≅ ∠3
1
4
2
3
6. Given: QX  NS , 1  3
Prove: 2  4
4
N
7. Given: FDE and FBC are supplementary,
Prove: FDE  FBA
Homework 3: Parallel Lines
For each of the diagrams below, find the value of x makes
1.
1 ||  2?
2.
Use the diagram below to answer questions 4 and 5.
4. Name the segments, if any, that are parallel if ∠6 ≅
∠9.
5. Name the segments, if any, that are parallel if ∠1 ≅
∠9.
̅̅̅̅̅̅ ∥ 𝐶𝐷𝐸
̅̅̅̅̅̅ , and 𝐹𝐷
̅̅̅̅ bisects
6. In the accompanying diagram, 𝐴𝐹𝐵
∠𝐶𝐹𝐵. Which statement must be true?
(1) ∠𝑤 ≅ ∠𝑦
(3) ∠𝑤 ≅ ∠𝑧
(2) ∠𝑦 ≅ ∠𝑧
(4) ∠𝑥 ≅ ∠𝑦
7. Given: 𝑟 ∥ 𝑡
Prove: ∠8 ≅ ∠1
3.
8. Given: ̅̅̅̅
𝐴𝐷 ∥ ̅̅̅̅
𝐵𝐶 , ̅̅̅̅
𝐵𝐷 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐴𝐵𝐶
Prove: ∠𝐴𝐷𝐵 ≅ ∠𝐴𝐵𝐷
A
D
B
C
̅̅̅̅, ∠𝑄𝑆𝑇 ≅ ∠1
̅̅̅̅ ∥ 𝑆𝑇
9. Given: 𝑃𝑅
Prove: ∠𝑃𝑄𝑆 ≅ ∠1
1
Homework 4: Proving Lines Parallel
1. Use the figure below to name the
given angles.
2. In the accompanying diagram,
l
parallel lines and
m are cut by
transversal t.
a. Name a pair of corresponding
angles
b. Name a pair of alternate interior
angles
Which statement is true?
A) 𝑚∠1 + 𝑚∠3 = 𝑚∠4 + 𝑚∠5
B) 𝑚∠1 + 𝑚∠2 = 𝑚∠2 + 𝑚∠3
C) 𝑚∠1 + 𝑚∠2 + 𝑚∠5 = 360°
D) 𝑚∠1 + 𝑚∠2 + 𝑚∠3 = 180°
̅̅̅̅, 𝑚∠7 = (2𝑥 − 5)°,
3. In the diagram to the right ̅̅̅̅
𝐷𝐶 ||𝐴𝐵
𝑚∠8 = (2𝑥 + 6)°, and 𝑚∠6 = (3𝑥 − 1)°. What is 𝑚∠6?
4. Given:
5. Given
Prove:
Prove:
STATEMENT
REASON
STATEMENT
REASON
6. Given: <1  <3
<2  <4
̅̅̅̅
Prove: ̅̅̅̅
𝑃𝑄 || 𝑅𝑆
7. Given:
Prove:
Homework 5: More Parallel Line Proofs
Use the diagram to the right answer questions 1 – 3.
1. If ∠3 ≅ ∠10 can be used to prove lines parallel,
a. Name the pair of parallel lines _________________
b. State the theorem/corollary that you would use to prove that the lines were
parallel.
______________________________________________________________________________
______________________________________________________________________________
2. If ∠1 ≅ ∠12 can be used to prove lines parallel,
a. Name the pair of parallel lines _________________
b. State the theorem/corollary that you would use to prove that the lines were
parallel.
______________________________________________________________________________
______________________________________________________________________________
3. If ∠15 ≅ ∠𝑆𝑅𝑄 can be used to prove lines parallel,
a. Name the pair of parallel lines _________________
b. State the theorem/corollary that you would use to prove that the lines were
parallel.
______________________________________________________________________________
______________________________________________________________________________
4. In the diagram to the right, ⃡𝐴𝐵 is parallel to ⃡𝐶𝐷, ⃡𝐴𝐸𝐷 is a
transversal and ̅̅̅̅
𝐶𝐸 is drawn. Find the value of x.
5. Given: 𝑚∠2 = 𝑚∠3
̅̅̅̅ ||𝑅𝑇
̅̅̅̅
Prove: 𝑈𝑄
7.
Given: 𝑅𝑇 bisects <QRS
𝑄𝑈 bisects <RQP
1  4
Prove: 𝑄𝑈 || 𝑅𝑇
8.
Given: <1  <2, 𝑚 ∥ 𝑛
Prove: <3  <4
4
2
13
t
n
m

Statement
Reason
Statement
Reason
Homework 6: Perpendicular Line Proofs
1. In the diagram to the
2. In the diagram to the
̅̅̅̅ ||𝑅𝑆
̅̅̅̅, what is
̅̅̅̅ ||𝐷𝐸
̅̅̅̅ , what is
below 𝑃𝑄
below 𝐴𝐶
the value of x?
the value of x?
1
p || q, t  p
Prove: t  q
1. Given:
t
Statement
Reason
̅̅̅̅ , ̅̅̅̅
̅̅̅̅
2. Given: ̅̅̅̅
𝐴𝐵  𝐸𝐹
𝐶𝐷  𝐸𝐹
Prove: <1  <2
1
2
p
2
3. In the diagram below,
̅̅̅̅ ⊥ 𝑆𝑇
̅̅̅̅ at R.
𝑙 ∥ 𝑚 and 𝑄𝑅
If 𝑚∠1 = 63, find 𝑚∠2.
3. Given:
Prove:
B
A
q
C
D
Statement
Reason
Homework 7: More Perpendicular Line Proofs
1. In the diagram below, lines n and m
are cut by transversals p and q.
What value of x would make lines n
and m parallel?
2. Line n intersects lines l and m,
forming the angles shown in the
diagram below. Which value of x
would prove
?
3. ⃡𝐴𝐵 intersects ⃡𝐶𝐷 at E, 𝑚∠𝐴𝐸𝐶 = 3𝑥 and 𝑚∠𝐴𝐸𝐷 = 5𝑥 − 60.
(a) Find the value of x.
(b) Show that ⃡𝐴𝐵 is perpendicular to ⃡𝐶𝐷.
4.
Given: CD || EF , AB  CD
Prove: mBGF  90 
A
D
C
E
G
B
F
5. Given: 1  2 , 3  4
Prove: 5  6
1 2
m
k
5
3 4
h
6
j
6. Given: h  f 1  2 ,
Prove: g || h
f
1
g
3
4
2
h
Homework 8: Mixed Practice
̅̅̅̅ ∥ 𝑃𝑄
̅̅̅̅ . Find
1. In the diagram below, 𝑆𝑅
𝑚∠1 and 𝑚∠2.
̅̅̅̅ and
2. In the diagram below, ̅̅̅̅
𝐸𝐴 ∥ 𝐵𝐷
𝑚∠𝑦 = 56. Find 𝑚∠𝑥.
3. Given: ∠𝐶𝐴𝐵 ≅ ∠𝐷𝐶𝐴 and ∠𝐷𝐶𝐴 ≅ ∠𝐸𝐶𝐵
Prove: (a) ⃡𝐹𝐺 ∥ ⃡𝐷𝐸
(b) ∠𝐶𝐴𝐵 ≅ ∠𝐶𝐵𝐴
̅̅̅̅ ⊥ ̅̅̅̅
4. Given: 𝑅𝑆
𝑅𝑄
̅̅̅̅ ⊥ 𝑅𝑄
̅̅̅̅
𝑃𝑄
̅̅̅̅
Prove: ̅̅̅̅
𝑃𝑄 ∥ 𝑅𝑆
5. Given:
Prove: