Question

1. what is the relationship between bx and cy? what conclusion can you draw about the relationship of \\( \triangle axb \\) and \\( \triangle cdy \\)? explain.

Explanation:

Step1: Analyze the angles and sides

In \(\triangle AXB\) and \(\triangle CDY\), \(AB = CD=3\mathrm{cm}\), \(\angle A = \angle D = 25^{\circ}\), \(\angle B=\angle C = 45^{\circ}\).

Step2: Use the Angle - Angle - Side (AAS) congruence criterion

The AAS congruence criterion states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
Since \(\angle A=\angle D\), \(\angle B = \angle C\) and \(AB = CD\), by AAS, \(\triangle AXB\cong\triangle CDY\).
Because the triangles are congruent, their corresponding parts are equal. So \(BX = CY\) (corresponding parts of congruent triangles).

Answer:

\(BX = CY\) and \(\triangle AXB\cong\triangle CDY\) (by AAS congruence criterion as \(\angle A=\angle D\), \(\angle B=\angle C\) and \(AB = CD\))