Mathematics

Grade9

Easy

Question

# The steps of a proof are shown.

Given is a complement of .

Prove is a complement of

What is reason 5?

Statements | Reasons |

1. ∠1 is a complement of ∠2. |
1. Given |

2. ∠2 ≡ ∠3 | |

3. m ∠ 1 + m ∠ 2 = 90° | |

4. m ∠ 2 = m ∠ 3 | |

5. m ∠ 1 + m ∠ 3 = 90° | |

6. ∠1 is a complement of ∠3. |

- Definition of complementary angles
- Substitution Property of Equality
- Definition of congruent angles
- Subtraction Property of Equality

Hint:

### in this question, given is ∠1 is complement of ∠2 and ∠2 ≅∠3, and here prove to ∠1 is a complement of ∠3. We have to give reason of step 5 . for that use the property of equality.

## The correct answer is: Substitution Property of Equality

### Here , we have to find that reason of step 5.

Firstly , we have is ∠1 is complement of ∠2 and ∠2 ≅∠3

And steps are,

∠1 is complement of ∠2 (given)

∠2 ≅∠3 (given)

m∠1 + m ∠2 = 90 ( complementary angle)

m ∠2 = m ∠3 ( both angle is congruent )

m ∠2 + m ∠3 = 90 ( substitution property )

∠1 is complement of ∠3

Therefore, the reason of step 5 is substitution property of equality.

The correct answer is Substitution property of Equality.

Or,

Substitution Property of Equality

The whole proof:

Statements
Reasons
1. ∠1 is a complement of ∠2.

1. Given
2. ∠2 ≡ ∠3
2. Given
3. m ∠ 1 + m ∠ 2 = 90°
3. Definition of complementary angles

4. m ∠ 2 = m ∠ 3
4. Definition of congruent angles
5. m ∠ 1 + m ∠ 3 = 90°
5. Substitution Property of Equality
6. ∠1 is a complement of ∠3.
6. Definition of complementary angles

In this question, we have to find the reason of step 5 which is substitution property. In substitution property of equality , if X = Y and X = Z then Y = Z.