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Chapter 5: Q17 (page 187)

GM炉is a median of right 螖IRG

If m鈭�1=32find the measures ofrole="math" localid="1637864336352" 鈭�2,鈭�3 and 鈭�4.

Short Answer

Expert verified

The measures of 鈭�2,鈭�3and鈭�4are 32,58and58respectively.

Step by step solution

01

Step 1. Description of step.

The length of the median is equal to half the length of the hypotenuse.

Therefore, RM=GM.

02

Step 2. Description of step.

Consider 螖RMG, in which RM=GMthen by isosceles triangle theorem, m鈭�1=m鈭�2=32.

Consider 螖IRGsuch that

m鈭�IGR=m鈭�2+m鈭�3=90

03

Step 3. Description of step.

Consider 螖IRGthen by an angle sum theorem,

m鈭�1+m鈭�2+m鈭�3+m鈭�4=18032+m鈭�2+m鈭�3+m鈭�4=18032+90+m鈭�4=180m鈭�4=180鈭�122=58

04

Step 4. Description of step.

Substitute 32 for m鈭�2into m鈭�2+m鈭�3=90to find the value of m鈭�3.

m鈭�2+m鈭�3=9032+m鈭�3=90m鈭�3=90鈭�32=58

Therefore, the measures of 鈭�2,鈭�3and鈭�4are 32,58and58respectively.

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Most popular questions from this chapter

For the following figure, if RE=EWthen name all angles congruent to 鈭�ERW.

In Exercise 5 quad. ABCD is a parallelogram. Find the values of x, y, and z.

Give the reason for each step in the following proof of theorem 5-6

Given: m鈭�A=m鈭�C=x;m鈭�B=m鈭�D=y

Prove: ABCD is a parallelogram.

Proof:

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-7.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD炉鈮�BC炉
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