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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 29 to 31, M and N are the midpoints of sides R S ¯ and R T ¯ of R S T , respectively.

Given: R M = R N = 2 x + 1
  S T = 5 x - 3
  m R = 60 °
Find: x , R M , and S T

To determine

To find:

x, RM, and ST

For RM=RN=2x+1

ST=5x-3

mR=60°

Explanation

Calculation:

Given,

RM=RN=2x+1

ST=5x-3

mR=60°

M and N are the midpoints of sides RS¯ and RT¯ OF RST respectively.

A line segment that joins the mid points of two sides of a triangle is parallel to the third sides and has a length equal to one-half the length of the third side.

Thus,

MN=12ST

MN=125x-3

Now, in RMN we have

mR=60°

But, RM=RN

Since, angle opposite to the equal sides are equal in measure,

mM=mN=xsay

By the angle sum property of a triangle in RMN

R+M+N=18O°

60°+x+x=180°

60°+2x=180°

Add; -60° on both sides,

60°+2x+-60°=180°+-60°

2x+60°+-60°=180°-60°

2x=120°

Divide; by 2 on both sides,

2x2=120°2

x=60°

Thus,

R=M=N=60°

Hence, RMN is an equilateral triangle

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