Question

show that the polygons are congruent by identifying all the congruent corresponding parts. then complete the congruence statement.

∠x ≅ ∠ select choice ;
∠y ≅ ∠ select choice ;
∠z ≅ ∠ select choice ;
segment xy ≅ segment select choice
segment xz ≅ segment select choice
segment yz ≅ segment select choice
△xyz ≅ △ select choice

Explanation:

Step1: Identify congruent angles

• $\angle X$ is a right angle ($90^{\circ}$), and $\angle A$ is also a right angle ($90^{\circ}$), so $\angle X\cong\angle A$.
• $\angle Y = 60^{\circ}$, and $\angle B=60^{\circ}$, so $\angle Y\cong\angle B$.
• $\angle Z = 30^{\circ}$, and $\angle C = 30^{\circ}$, so $\angle Z\cong\angle C$.

Step2: Identify congruent sides

• Segment $XY = 2.5$, and segment $AB = 2.5$, so segment $XY\cong$ segment $AB$.
• Segment $XZ = 4.3$, and segment $AC = 4.3$, so segment $XZ\cong$ segment $AC$.
• Segment $YZ = 5$, and segment $BC = 5$, so segment $YZ\cong$ segment $BC$.

Step3: Complete the congruence statement

Since all corresponding angles and sides are congruent, by the Side - Angle - Side (SAS) or Angle - Side - Angle (ASA) or Side - Side - Side (SSS) congruence criteria (in this case, we can use SSS as we have shown all three pairs of sides are congruent), $\triangle XYZ\cong\triangle ABC$.

Answer:

$\angle X\cong\angle A$; $\angle Y\cong\angle B$; $\angle Z\cong\angle C$; segment $XY\cong$ segment $AB$; segment $XZ\cong$ segment $AC$; segment $YZ\cong$ segment $BC$; $\triangle XYZ\cong\triangle ABC$