Question

1. which statements (if any) are true about the diagram? select all that apply: a. point q is the midpoint of line pt. b. \\( \angle pqs \\) and \\( \angle sqt \\) are supplementary. c. \\( \angle pqt \\) is a straight angle. d. none of these 31. which statements (if any) are true about the diagram? select all that apply: a. ray eb is an angle bisector. b. point e is the midpoint of line segment ac. c. \\( \angle aeb = 90 ^ { \circ } \\) d. none of these

Explanation:

Question 30

• Option A: For \(Q\) to be the mid - point of \(PT\), \(PQ = QT\). There is no information in the diagram to suggest this equality.
• Option B: \(\angle PQS\) and \(\angle SQT\) do not add up to \(180^{\circ}\) (supplementary angles sum to \(180^{\circ}\)).
• Option C: \(\angle PQT\) is a straight - line angle (a straight line forms an angle of \(180^{\circ}\)).

• Option A: An angle bisector divides an angle into two equal parts. There is no indication that \(\angle AEB=\angle BEC\).
• Option B: For \(E\) to be the mid - point of \(AC\), \(AE = EC\). There is no information in the diagram to suggest this equality.
• Option C: The right - angle symbol at \(\angle AEB\) indicates that \(\angle AEB = 90^{\circ}\).

Answer:

C. \(\angle PQT\) is a straight angle

Question 31