Question

in the rectangle abcd shown, x and y are mid - points of the sides. and dp = aq. acyp ≅ ahyq by aas. acyp ≅ ahyq by sss. so qy ≅ py by cpctc. what type of quadrilateral is pyqx? a. kite b. rhombus c. trapezoid d. parallelogram

Explanation:

Step1: Recall properties of congruent triangles

Given $\triangle CYP\cong\triangle AYQ$ by AAS or SSS and $QY = PY$ by CPCTC. Since $X$ and $Y$ are mid - points of sides of rectangle, we can find more equal - length sides.

Step2: Analyze the sides of quadrilateral PYQX

In rectangle $ABCD$, $X$ and $Y$ are mid - points. We know that opposite sides of a rectangle are equal. Also, from the congruence of triangles, we can show that $PX=QX$. In quadrilateral $PYQX$, we have $PY = QY$ and $PX=QX$. A quadrilateral with two pairs of adjacent sides equal is a kite.

Answer:

A. Kite