Question

given: rectangle abcd,
bp≅cp
prove: al≅dm

1. rectangle abcd,

bp≅cp

1. ∠pbc≅∠pcb
2. bc∥ad
3. given

2.

1. if two lines form congruent alternate interior angles when cut by a transversal.

Explanation:

Step1: Use the property of congruent sides in a triangle

In \(\triangle PBC\), since \(\overline{BP}\cong\overline{CP}\), by the isosceles triangle theorem (if two sides of a triangle are congruent, then the angles opposite those sides are congruent), we have \(\angle PBC\cong\angle PCB\).

Step2: Use the property of a rectangle

For rectangle \(ABCD\), by the definition of a rectangle (a parallelogram with four right - angles, and in a parallelogram, opposite sides are parallel), we know that \(\overline{BC}\parallel\overline{AD}\).

Answer:

1. Isosceles triangle theorem; 3. Definition of a rectangle.