Question

If it is given that AX = 3.5, what is the length of YZ?
a) 2.5
b) 3.0
c) 3.5

Answer 1

The length of YZ is 3.5. Option (c) is true.

Explanation:

The Triangle Midsegment Theorem states that:

In any triangle, the segment connecting the midpoints of any two sides is parallel to the third side and half its length.

Midsegment: A segment connecting the midpoints of two sides of a triangle.

Parallel: The midsegment runs parallel to the third side of the triangle.

Half the length: The length of the midsegment is half the length of the third side.

From the figure:

The point X is the midpoint of AB.

So,

AX = BX

And:

AB = AX + BX

AB = 2AX

AB = 2 x 3.5

AB = 7

Now,

Applying the Triangle Midsegment Theorem:

YZ = AB/2

YZ = 7/2

YZ = 3.5

Thus, option (c) is true.