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Neko [114]
3 years ago
9

GJ is a midsegment of triangle DEF, and HK is a midsegment of triangle GFJ. What is the length of HK?

Mathematics
1 answer:
loris [4]3 years ago
7 0

Answer:

Option B) 4 centimeters

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the value of n

we know that

a) GJ is a midsegment of triangle DEF

then

G is the midpoint segment DF and J is the midpoint segment EF

DG=GF and EJ=JF

b) HK is a midsegment of triangle GFJ

then

H is the midpoint segment GF and K is the midpoint segment JF

GH=HF and JK=KF

In this problem we have

HF=7 cm

so

GH=7 cm

GF=GH+HF ----> by addition segment postulate

GF=7+7=14 cm

Remember that

DG=GF

substitute the given values

2n-1=14

solve for n

2n=14+1

2n=15

n=7.5\ cm

step 2

Find the length of GJ

we know that

The <u><em>Midpoint Theorem</em></u> states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

so

GJ=\frac{1}{2}DE

we have

GE=2n+1=2(7.5)+1=16\ cm

substitute

GJ=\frac{1}{2}16=8\ cm

step 3

Find the length of HK

we have that

HK=\frac{1}{2}GJ ----> by the midpoint theorem

we have

GJ=8\ cm

substitute

HK=\frac{1}{2}8=4\ cm

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