Question

Decide whether there is enough information to prove that △WXZ≅△YZX using the SAS Congruence Theorem.

A: yes; Because ZW≅XY, ∠W≅∠Y, and WX≅YZ, the two triangles are congruent by the SAS Congruence Theorem
B: yes; Because ZW≅XY, ∠W≅∠Y, and ZX≅XZ, the two triangles are congruent by the SAS Congruence Theorem.
C: no; There is one pair of congruent sides and one pair of congruent angles, but there is no other pair of congruent sides.
D: no; There are two pairs of congruent sides and one pair of congruent angles, but the angles are not the included angles.

Answer 1

D

Explanation:

From the triangle, we can see that:

`ZW\cong XY, \angle W\cong \angle Y\text{ and } ZX\cong XZ`

However, note that the angle is not between the two sides. Therefore, we cannot use SAS congruence.

Instead, this is SSA, which cannot prove congruence.

A is incorrect because we cannot say that WX is congruent to YZ from the given information.

B is incorrect because SAS cannot be applied.

C is incorrect because there is indeed another pair (ZX and XZ).

D is correct because there are two pairs of congruent sides and one pair of congruent angles, but the angles are not included (they are not between the sides). Hence, SAS cannot be applied and congruence cannot be proved.