Question

Delmar is constructing an equilateral triangle. He uses his straightedge to draw a segment and labels the endpoints W and X. With the compass opening equal to the length of the segment, he draws a circle centered at point W and then a circle centered at point X. He labels the intersections of the circles as points P and Q.

How should Delmar finish the construction?

Responses

Use a straightedge to join points P and Q. Label the intersection of PQ¯¯¯¯¯
and WX¯¯¯¯¯¯
as A. Construct the midpoint of AX¯¯¯¯¯
and label it B. Use a straightedge to join points Q and B. △QAB
is equilateral.
Use a straightedge to join points P and Q . Label the intersection of P Q ¯ and W X ¯ as A . Construct the midpoint of A X ¯ and label it B . Use a straightedge to join points Q and B . △ Q A B is equilateral.

Use a straightedge to join points W and P and then points P and X. △WPX
is equilateral.
Use a straightedge to join points W and P and then points P and X . △ W P X is equilateral.

Use a straightedge to join points W and P, P and Q, and then W and Q. △WPQ
is equilateral.
Use a straightedge to join points W and P , P and Q , and then W and Q . △ W P Q is equilateral.

Use a straightedge to join points P and Q. Label the intersection of PQ¯¯¯¯¯
and WX¯¯¯¯¯¯
as A. Use a straightedge to join points Q and X. △QAX
is equilateral.

Answer 1

Join W to P and P to X with the straightedge. Triangle WPX is equilateral because WP = WX (P lies on the circle centered at W with radius WX) and PX = WX (P lies on the circle centered at X), so WP = PX = WX.