Question

Which statement describes the two steps necessary to prove that point Q is the midpoint of segment AB?

A. Show that AQ = QB; show that AQ = 2AB, and BQ = 2AB.
B. Show that A, Q, and B are collinear; show that AQ + QB = AB.
C. Show that AQ = QB; show that ∠QAB≅∠QBA.
D. Show that A, Q, and B are collinear; show that AQ = QB

Answer 1

To prove that point Q is the midpoint of segment AB, one must show that points A, Q, and B are collinear and that the segments AQ and QB are equal in length.

Step-by-step explanation:

The question is asking which steps are needed to prove that point Q is the midpoint of segment AB. The correct steps involve proving two key things: that point Q is collinear with points A and B, and that the distances from A to Q and from Q to B are equal. So, we need a two-step process where the first step is to show that points A, Q, and B are on the same straight line (collinear), and the second step is to demonstrate that the distances from A to Q (AQ) and B to Q (BQ) are the same.

As per the options provided, the correct answer would be:

D. Show that A, Q, and B are collinear; show that AQ = QB.

This option correctly identifies the two necessary steps to prove Q is the midpoint: confirming that the points lie on a straight line and that the segments on either side of Q are equal in length.