Question

1. t is the midpoint of \\(\overline{pq}\\). which one of the following is not an appropriate statement?

a. \\(pt = tq\\) b. \\(\overline{pt} = \overline{tq}\\) c. \\(\overline{pt} \cong \overline{tq}\\)
d. \\(pt + tq = pq\\)

1. which letter has rotational symmetry?

a. s b. d c. l d. u

Explanation:

Question 17

Step1: Recall Midpoint Properties

A midpoint \( T \) of segment \( \overline{PQ} \) means \( PT = TQ \) (lengths are equal), \( \overline{PT} \cong \overline{TQ} \) (segments are congruent), and \( PT + TQ = PQ \) (segment addition postulate).

Step2: Analyze Each Option

• Option a: \( PT = TQ \) (lengths equal, valid).
• Option b: \( \overline{PT} = \overline{TQ} \) (segments are not equal as objects, only their lengths or congruence is defined; invalid).
• Option c: \( \overline{PT} \cong \overline{TQ} \) (segments congruent, valid).
• Option d: \( PT + TQ = PQ \) (segment addition, valid).

Question 18

Step1: Define Rotational Symmetry

A figure has rotational symmetry if it maps onto itself after a rotation (less than \( 360^\circ \)).

Step2: Analyze Each Letter

• Option a: "S" rotated \( 180^\circ \) maps onto itself (rotational symmetry).
• Option b: "D" has reflection symmetry, not rotational (except \( 360^\circ \)).
• Option c: "L" has no rotational symmetry (except \( 360^\circ \)).
• Option d: "U" has reflection symmetry, not rotational (except \( 360^\circ \)).

Answer:

b. $\overline{PT} = \overline{TQ}$