McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Standardized Test Practice

Exercise 7 Page 331

What is the operation used in that step of the proof?

Subtraction Property of Equality

Practice makes perfect

We are given a two-column proof and asked to give a justification to move between the following two statements.

Justification

Let's begin by looking at the first piece of the given information. m∠ A+46&=90 m∠ A+46-46&=90-46In this step we are subtracting 46 from both sides of the equation. This is justified by the Subtraction Property of Equality. Ifa=b, thena-c=b-c.

Completed Proof

Given:& ∠ A is the complement of∠ B & m∠ B=46 Prove:& m∠ A=44 Proof:

Statements
Reasons
1.
∠ A is the complement of ∠ B
m∠ B=46
1.
Given
2.
m∠ A+m∠ B=90
2.
Definition of complementary angles
3.
m∠ A+46=90
3.
Substitution Property of Equality
4.
m∠ A+46-46=90-46
4.
Subtraction Property of Equality
5.
m∠ A=44
5.
Substitution Property of Equality