Question

The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.

A. ⎯⎯⎯⎯⎯⎯⎯⎯
≅ ⎯⎯⎯⎯⎯⎯⎯⎯
B. ⎯⎯⎯⎯⎯⎯⎯⎯
≅ ⎯⎯⎯⎯⎯⎯⎯⎯⎯
C. ∠=90∘
D. ∠≅∠

Answer 1

In the given image, BC equals AD and ∠ABC measures 90°, confirming parallelogram properties. However, assertions about AP = CP and ∠CAD = ∠ACB lack sufficient evidence from the image.

Here are all the statements that must be true:

* BC = AD: This is a property of parallelograms. Opposite sides of a parallelogram are always congruent.

* ∠ABC = 90°: This is also a property of parallelograms. Diagonals of a parallelogram bisect each other at right angles.

The other statements are not necessarily true:

* AP = CP: There is not enough information in the image to determine whether this is true. We only know that the diagonals intersect at point P, but we don't know the lengths of AP and CP.

* ∠CAD = ∠ACB: These angles are not necessarily congruent. In fact, there is no reason to believe they are equal or related in any way.