Question

In the given figures, the congruent parts have been shown by identical marks. From the figures of □XYZW and □PQRS, write


(1) two pairs of congruent segments.
(2) two pairs of congruent angles.
(3) whether the statement □XYZW ≅ □PQRS is true or false. Give reasons for your answer.

Answer 1

(1) We have the following pairs of congruent segments:
Seg XY ≅ Seg PQ, Seg XY ≅ Seg PS, Seg XY ≅ Seg SR, Seg XY ≅ Seg QR
Seg XW ≅ Seg PS, Seg XW ≅ Seg SR, Seg XW ≅ Seg QR, Seg XW ≅ Seg PQ
Seg WZ ≅ Seg SR, Seg WZ ≅ Seg QR, Seg WZ ≅ Seg PQ, Seg WZ ≅ Seg PS
Seg YZ ≅ Seg QR, Seg YZ ≅ Seg PQ, Seg YZ ≅ Seg PS, Seg YZ ≅ Seg SR
We can choose any two pairs.

(2) We have the following pairs of congruent angles:
∠X ≅ ∠P, ∠X ≅ ∠Q, ∠X ≅ ∠R, ∠X ≅ ∠S
∠Y ≅ ∠Q, ∠Y ≅ ∠R, ∠Y ≅ ∠S, ∠Y ≅ ∠P
∠Z ≅ ∠R, ∠Z ≅ ∠S, ∠Z ≅ ∠Q, ∠Z ≅ ∠P
∠W ≅ ∠S, ∠W ≅ ∠P, ∠W ≅ ∠Q, ∠W ≅ ∠R
We can choose any two pairs.

(3) □XYZW ≅ □PQRS. This statement is true because all the sides and angles of □XYZW are equal to the all the sides and angles of □PQRS.