Page 196 - Math Course 2 (Book 2)

Two-Column Algebraic Proof

Geometric Proof

DRIVING
A stop sign as shown below is a regular octagon. If the measure of angle A is 135 and angle A is
congruent to angle G, prove that the measure of angle G is 135.

A. Symmetric Property Proof:
B. Substitution
C. Transitive Property Statements Reasons
D. Subtraction Property
1. m∠A = 135 1. Given

2. ∠A ≅ ∠G 2. Given

3. m∠A = m∠G 3. Definition of congruent angles
Answer
4. m∠G = 135 4. ______?______

Skill Practice!

State the property that justifies each statement.

1. If 80 = m∠A, then m∠A = 80. 4. If VR + TY = EN + TY, then VR = EN.

2. If RS = TU and TU = YP, then RS = YP.
5. If m∠1 = 30 and m∠1 = m∠2, then m∠2 = 30.
3. If 7x = 28, then x = 4.

Complete the following proof.
6. Given: 8x – 5 = 2x + 1
Prove: x = 1
Proof:

Statements Reasons

a. 8x – 5 = 2x + 1 a.

b. 8x – 5 = 2x = 2x + 1 – 2x b.

c. c. Substitution Property

d. d. Addition Property

e. 6x = 6
6x 6
f. = 6
6
g.

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