Question

A. Find the length of the midsegment of an equilateral triangle with side lengths of 12.5 cm.

b. Given that UT is the perpendicular bisector of line segment AB, where T is on AB, find the length of AT given AT = 3x + 6 and TB = 42 - x.

c. Given angle EFG has angle bisector FH, where EF = GF, find the value of y if EH = 5y + 10 and HG = 28 - y.

Answer 1

• a. 6.25
• b. AT = 33
• c. y = 3

Explanation:

a. Midsegment is half the length of the parallel side:

• 12.5/2 = 6.25

b. Segment addition postulate:

• AB = AT + TB = 3x + 6 + 42 - x = 2x + 48

Perpendicular bisector of segment divides the segment in two equal halves:

• AT = TB
• 3x + 6 = 42 - x
• 4x = 36
• x = 9

AT is:

• AT = 3*9 + 6
• = 33

c) The point on the angle bisector H is equidistant from the point E and G:

• EH = HG
• 5y + 10 = 28 - y
• 5y + y = 28 - 10
• 6y = 18
• y = 3