Question

Write Given and Provestatements for the Midpoint Theorem, as inferred from the statement above. The Midpoint Theorem: If M midpoint of XY. then XM =1/2 XY and MY = 1/2xy

Answer 1

The Midpoint Theorem implies if M is the midpoint of a segment XY, then XM = ½XY and MY = ½XY, dividing XY into two equal parts. To prove this, we assert that M is equidistant from X and Y, and thus XM and MY are each half of XY.

Step-by-step explanation:

The Midpoint Theorem states that if M is the midpoint of a segment XY, then XM and MY are equal to half the length of XY. To apply the Midpoint Theorem, we start by defining the Given and Prove statements.

Given: M is the midpoint of XY.
Prove: XM = ½XY and MY = ½XY.

We know from the definition of a midpoint that M divides XY into two equal parts. This implies that XM = MY.

Since M is equidistant from both X and Y, the total length of XY is simply two times the length of XM or MY.

Therefore, XM and MY must each be half the length of XY (i.e., XM = ½XY and MY = ½XY).