Question

1. 2)triangle xyz with vertices x (2,4), y (-2,4), z (4,8) is translated 5 units to the right to form triangle xy z select true or false for each statement

	true	false
triangle xyz and triangle xy z are similar and congruent	○	○
triangle xyz and triangle xy z are similar but not congruent	○	○
true false side xy is shorter than side xy	○	○
the perimeter is the same.	○	○

Explanation:

Step1: Recall Translation Properties

Translation is a rigid transformation, so it preserves side lengths and angles. Congruent figures have same shape and size; similar figures have same shape (angles) and proportional sides (ratio 1 for congruent).

Step2: Analyze First Statement

Since translation preserves size and shape, \( \triangle XYZ \) and \( \triangle X'Y'Z' \) are congruent (hence similar, as congruent implies similar with ratio 1). So "similar and congruent" is True.

Step3: Analyze Second Statement

As they are congruent, they can't be "similar but not congruent". So this is False.

Step4: Analyze Third Statement

Translation preserves side lengths, so \( X'Y' = XY \). Thus "shorter" is False.

Step5: Analyze Fourth Statement

Perimeter is sum of sides. Since sides are preserved, perimeters are equal. So "perimeter same" is True.

Answer:

• Triangle XYZ and triangle X′Y′Z′ are similar and congruent: True (select True circle)
• Triangle XYZ and triangle X′Y′Z′ are similar but not congruent: False (select False circle)
• Side X′Y′ is shorter than side XY: False (select False circle)
• The perimeter is the same: True (select True circle)