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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Chapter Review

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Exercise 22 Page 490

What do we know about complementary angles?

See solution.

Practice makes perfect

We are told that ∠ 3 and ∠ 2 are complementary angles and that the measures of ∠ 1 and ∠ 2 add to 90^(∘). We want to prove that ∠ 3 and ∠ 1 are congruent angles. To do so, we will do a Flowchart Proof. Let's write the given information!

Since ∠3 and ∠2 are complementary angles, the sum of their measures is 90^(∘).

Using the Transitive Property of Equality, we can equate m∠ 3 + m∠ 2 to m∠ 1 + m∠ 2.

By the Subtraction Property of Equality, if we subtract m∠ 2 from both sides of the last equation, we can conclude that m∠ 3 = m∠ 1.

Finally, by the definition of congruent angles, we know that ∠3 is congruent to ∠ 1.

Therefore, ∠3 and ∠ 1 are congruent angles. The proof is complete.

Subchapter links

1 Conditional Statements p.488

2 Inductive and Deductive Reasoning p.488

3 Postulates and Diagrams p.489

4 Proving Statements about Segments and Angles p.490

5 Proving Geometric Relationships p.490