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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掳.

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掳consider a right-angle triangle 螖ABCsuch that 鈭�A=90掳. Since, sum of three angles of a triangle is 180掳, therefore,

鈭�A+鈭�B+鈭�C=180掳90掳+鈭�B+鈭�C=180掳90掳+鈭�B+鈭�C鈭�90掳=180掳鈭�90掳鈭�B+鈭�C=90掳

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


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Most popular questions from this chapter

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If two lines intersect to form right angles, then the lines are perpendicular.

State the postulate or theorem that justifies each statement.

鈭�3鈮�鈭�6

Find the values of x and y that make the lines shown in red parallel.

Fold a corner of a sheet of paper and then cut along the fold to get a right triangle. Let the right angle be 鈭�C. Fold each of the other two vertices so that they coincide with point. What result of this section does this illustrate?

In each exercise some information is given. Use this information to name the segments that must be parallel. If there are no such segments, say so.

m鈭�1=m鈭�8
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