1. Proving statements about angles
BIG IDEA: Reasoning and Proof
ESSENTIAL UNDERSTANDING
Given information, definitions, properties, postulates, and previously proven theorems can be used as reasons in a proof.
MATHEMATICAL PRACTICE
Construct viable arguments and critique the reasoning of others.
Proving statements about angles

2. Getting Ready
A quilter wants to duplicate this quilt but knows the measure of only two angles. What are the measures of angles 1, 2, 3, and 4? How do you know?

3. Math Background
In a sense, proofs are problems in which the answer is already known and the focus is on demonstrating how the answer is derived using principles of deductive reasoning and related definitions, properties, postulates, and theorems.
In writing proofs, you will communicate your reasoning clearly to others using the two-column proof.

4. Theorems Right Angle Congruence Theorem Congruent Supplements Theorem
All right angles are ____________________
Congruent Supplements Theorem
If two angles are ______________________ of the same angle (or of congruent angles), then the two angles are __________________
Congruent Complements Theorem
Vertical Angles Theorem
Vertical angles are ____________________
Theorem: If two angles are _______________ and ____________________, then each is a ____________ angle

5. EX 1
Find the measures of the angles in the diagram given.

6. EX 2
Complete the statements given that 1. 2. 3. 4. 5. 6.

7. EX 3
Given:
Prove:
Statements
Reasons

8. EX 4
Given:
Prove:
Statements
Reasons 1. 2. 2 3. 4.

9. EX 5 Given: Prove: Statements Reasons 1 2
2 Definition of Supplementary Angles 3 4
4 Given 5 6
6 Subtraction Property 7

10. 2.6 p , 12 – 18 all, 20 – 30 evens, 33 – 36 all, 38 – 45 all
26 questions