Download Angle Proofs Packet - White Plains Public Schools

Angle
Proofs
Name: _________________
Period: ______
Teacher: _______________
Table of Contents
Day 1: SWBAT Recognize complementary and supplementary angles and prove angles
congruent by means of four new theorems
Pages 2-8
HW: pages 9-11
Day 2: SWBAT Write two-column angle proofs involving supplementary and
complementary angles
Pages 12-14
HW: pages 15-16
Day 3: SWBAT Write two-column angle proofs involving supplementary and
complementary angles
Pages 17-19
HW: pages 20-23
Day 4: REVIEW
Day 5: Exam
Angle Theorems
 If two angles are right angles, then they are congruent.
 If two angles are vertical angles, then they are congruent.
 If two angles are complements of the same angle, then they are congruent.
 If two angles are congruent, then their complements are congruent.
 If two angles are supplements of the same angle, then they are congruent.
 If two angles are congruent, then their supplements are congruent.
 If two angles form a linear pair, then they are supplementary
 If two angles are vertical angles, then they are congruent.
Additional Theorem:
Radii of a circle are congruent.
Radii of congruent circles are congruent.
1
Name________________________
Date_________________________
Geometry
Day1: Proofs with Angles
SWBAT: Recognize complementary and supplementary angles and prove angles congruent
by means of four new theorems
Warm - Up
2
Example 1:
You Try It!
Given:
Prove:
CONV: If the sum of two s is a straight  (180), then they are supplementary.
3
Example 2:
2.
4
3.
4.
When to use these theorems???
When 2 pairs of angles are complementary or supplementary to the SAME angle or
CONGRUENT angles.
Strategy: In statements, look for double use of the word “complementary” or “supplementary”
AND for a congruence statement. Circle the angles indicated by the congruence statement, and
the uncircled angles will be congruent! You don’t even need to look at a diagram!
5
Practice Proof Writing
1.
2. Given: 1  4
Prove: 2  3
6
O
3. Given: OA and MP intersect at T
Prove: 1  2
M
1
T
2
P
A
Summary
7
Exit Ticket
K
R
P
Given:
KMR  POR
Prove: ROM  RMO
Statement
O
M
Reason
8
Day 1 - Homework
1. Given:
1  2
Prove: 3  4
2.
Given: 2  4
Prove: 1  3
1
2
3
4
9
3. Given:
Prove:
O is complementary to 2
J is complementary to 1
O  J
4.
10
5.
T
6. Given: TR  RQ
TS  SQ
3  4
Prove: 1  2
R
2
4
1
3
S
Q
11
Name________________________
Date_________________________
Geometry
Day2: More Practice
Writing Proofs with Angles
SWBAT: Write two-column angle proofs involving supplementary and complementary angles.
Warm - Up
12
1.
Given: F is complementary to FGJ
H is complementary to HGJ
GJ Bisects FGH
Prove: F  H
2. Given:
Prove:
FKJ is a right angle.
HJK is a right angle
GKJ  GJK
FKG  HJG
13
3)
4)
14
Day 2 - Homework
5)
15
7)
8)
16
Name________________________
Date_________________________
Geometry
Day3: More Practice
Writing Proofs with Angles
SWBAT: Write two-column angle proofs involving supplementary and complementary angles.
Warm -Up
17
1.
2.
18
3.
4.
19
Day 3 - Homework
5.
6.
20
7.
8. Given:
Prove:
21
9.
22
10.
23