Question

what are the corresponding parts of the figures below? select all that apply. ( angle g cong angle t ), ( overline{hi} cong overline{qr} ), ( angle j cong angle s ), ( angle i cong angle t )

Explanation:

To determine the corresponding parts, we analyze the congruent angles and sides based on the markings (angles with the same number of arcs are congruent, and sides with the same length are congruent).

Step 1: Analyze \(\angle G \cong \angle T\)

• \(\angle G\) and \(\angle T\) have the same single arc marking, so they are congruent. This is correct.

Step 2: Analyze \(\overline{HI} \cong \overline{QR}\)

• The length of \(\overline{HI}\) is \(13\) ft, and the length of \(\overline{QR}\) is \(13\) ft. Since their lengths are equal, \(\overline{HI} \cong \overline{QR}\). This is correct.

Step 3: Analyze \(\angle J \cong \angle S\)

• \(\angle J\) and \(\angle S\) have the same double arc marking, so they are congruent. This is correct.

Step 4: Analyze \(\angle I \cong \angle T\)

• \(\angle I\) has a double arc marking, while \(\angle T\) has a single arc marking. They do not have the same marking, so \(\angle I

ot\cong \angle T\). This is incorrect.

Answer:

The correct corresponding parts are \(\boldsymbol{\angle G \cong \angle T}\), \(\boldsymbol{\overline{HI} \cong \overline{QR}}\), and \(\boldsymbol{\angle J \cong \angle S}\). The option \(\angle I \cong \angle T\) is incorrect. So the correct selections are:

• \(\angle G \cong \angle T\)
• \(\overline{HI} \cong \overline{QR}\)
• \(\angle J \cong \angle S\)