Question

which trapezoid is congruent to trapezoid t?
a. trapezoid y is congruent to trapezoid t because trapezoid t can be rotated and translated to create trapezoid y.
b. trapezoid x is congruent to trapezoid t because trapezoid t can be rotated and translated to create trapezoid x.
c. trapezoid w is congruent to trapezoid t because trapezoid t can be dilated and translated to create trapezoid w.
d. trapezoid z is congruent to trapezoid t because trapezoid t can be reflected and dilated to create trapezoid z.

Explanation:

Step1: Understand congruent shapes

Congruent shapes have the same size and shape. Transformations like rotation, translation, and reflection do not change the size of a shape. Dilation changes the size.

Step2: Analyze each option

• Option A: Trapezoid \(Y\) is smaller than \(T\). Dilation (not just rotation and translation) would be needed to change size, so \(Y\) is not congruent.
• Option B: Trapezoid \(X\) has the same size and shape as \(T\). Rotation and translation can map \(T\) to \(X\) without changing size.
• Option C: Trapezoid \(W\) is larger than \(T\). Dilation (changes size) is involved, so \(W\) is not congruent.
• Option D: Trapezoid \(Z\) is larger than \(T\). Dilation (changes size) is involved, so \(Z\) is not congruent.

Answer:

B. Trapezoid \(X\) is congruent to trapezoid \(T\) because trapezoid \(T\) can be rotated and translated to create trapezoid \(X\).