Question

If H is the midpoint of GE and J is the midpoint of FE, determine the following lengths.

Answer 1

Using the triangle midsegment theorem,

`4x-4=2(x+3) \implies 4x-4=2x+6 \implies x=5 \\ \\ \therefore HJ=8, JE=4`

Answer 2

HJ = 8

JE = 4

Explanation:

Theorem:

In a triangle, a segment that has as endpoints the midpoints of two sides is parallel and half the length of the third side.

Segment HJ has as endpoints points H and J which are midpoints of two sides of triangle EFG, so the length of segment HJ is half the length of the third side, segment FG.

HJ = (1/2)FG

x + 3 = (1/2)(4x - 4)

x + 3 = 2x - 2

5 = x

x = 5

HJ = x + 3 = 5 + 3 = 8

JE = x - 1 = 5 - 1 = 4