Question

in the figure, xywz is an isosceles trapezoid. which pair of triangles can be proved to be congruent with the result that \\( \angle zyx \cong \angle wxy \\) by cpctc? ( \triangle xzy ) and ( \triangle ywx ) ( \triangle xzp ) and ( \triangle ywp ) ( \triangle zpw ) and ( \triangle ypx ) ( \triangle xzw ) and ( \triangle ywz )

Explanation:

Step1: Properties of isosceles trapezoid

In isosceles trapezoid \(XYWZ\), \(XZ = YW\) (diagonals of isosceles trapezoid are equal), \(ZY=WX\) (legs of isosceles trapezoid are equal), and \(XY\) is common side.

Step2: Prove congruence by SSS

For \(\triangle XZY\) and \(\triangle YWX\), we have \(XZ = YW\), \(ZY = WX\), \(XY=YX\). By SSS (Side - Side - Side) congruence criterion, \(\triangle XZY\cong\triangle YWX\).

Step3: Use CPCTC

By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \(\angle ZYX\cong\angle WXY\).

Answer:

\(\triangle XZY\) and \(\triangle YWX\)