Question

g.3

1. parallelogram wtpy is shown below. it goes through a translation of 7 units left and 23 units up in order to create parallelogram hrzs. which statements must be true? select two correct answers.

a. line segment tp is congruent to line segment sz.
b. the measure of angle t equals the measure of angle r.
c. the measure of angle z is greater than the measure of angle p.
d. the length of side zs is 14 units more than the length of side py.
e. the perimeter of parallelogram hrzs is equal to the perimeter of parallelogram wtpy.
g.8

1. what is the approximate distance between points j and l? show your work.

Explanation:

Step1: Recall translation properties

A translation is a rigid transformation, so it preserves side lengths, angle measures, congruence of segments, and perimeter of the figure.

Step2: Analyze each option

• Option A: Since translation preserves segment congruence, $TP \cong SZ$ (as $TP$ maps to $SZ$). This is true.
• Option B: Angle $T$ maps to angle $R$ in the translation, so their measures are equal. This is true.
• Option C: Translation preserves angle measures, so $m\angle Z = m\angle P$. This is false.
• Option D: Translation preserves side lengths, so $ZS = PY$. This is false.
• Option E: Translation preserves side lengths, so perimeters are equal. This is true.

(Note: The question asks for two correct answers; A, B, E are all true, but A and B are direct congruence/angle preservation results, or A and E, but A and B are clear direct matches.)

Answer:

A. Line segment TP is congruent to line segment SZ.
B. The measure of angle T equals the measure of angle R.