Question

In the diagram below of triangle EFG, H is the midpoint of EG and I is the midpoint of FG. If HI = -4x + 45, and EF = 25 + 5x, what

is the measure of HI?

Answer 1

The value of line segment HI is 25

The Midpoint Theorem states that in a triangle, a line segment joining the midpoints of two sides is parallel to the third side and is half its length.

Since line HI is the line segment joining midpoint of GE and GF, then HI is parallel to EF and it is half of EF.

Therefore,

2 × (-4x + 45) = 25+5x

= -8x + 90 = 25 + 5x

- 13x = -65

x = -65/-13

x = 5

Therefore,

HI = -4x + 45

= -4(5) + 45

= 45 - 20

= 25

HI = 25