Question

in the rectangle abcd shown, x and y are mid - points of the given sides and dp = aq.
a) what type of quadrilateral is pyqx? prove your answer.
b) if points p and q are moved at a constant rate and in the same direction along dc and ad, respectively, does this change your answer in part a)? why or why not?
a) what type of quadrilateral is pyqx? prove your answer. first, given that dx = ax, ∠d and ∠a are right angles, and dp = aq, which of the following can be concluded?
a. △cyp≅△byq by sss
b. △pdx≅△qax by sas
c. △pdx≅△qax by sss
d. △cyp≅△byq by sas

Explanation:

Step1: Analyze congruent - triangle conditions

In rectangle \(ABCD\), \(X\) is the mid - point of \(AD\), so \(DX = AX\). \(\angle D=\angle A = 90^{\circ}\), and \(DP = AQ\). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle PDX\cong\triangle QAX\).

Answer:

B. \(\triangle PDX\cong\triangle QAX\) by SAS