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Chapter 3: Q8 (page 96)

Explain how each corollary of Theorem 3-11 follows from the theorem

Corollary 4

Short Answer

Expert verified

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Step by step solution

01

Step 1. State Theorem 3-11

Theorem 3-11 states that the sum of the angles is 180°.

02

Step 2. Statement of corollary 4

Corollary 4- Acute angles of a right triangles are complementary.

03

Step 3. Illustrate for Triangle ABC

In order to show that acute angles of a right triangles are complementary that is., sum of their measures is 90°consider a right-angle triangle ΔABCsuch that ∠A=90°. Since, sum of three angles of a triangle is 180°, therefore,

∠A+∠B+∠C=180°90°+∠B+∠C=180°90°+∠B+∠C−90°=180°−90°∠B+∠C=90°

As angles∠B and∠B are acute and complementary angles therefore, it can be concluded that acute angles of right triangle are complementary.


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