Question

Amazing isn't it? 100 points just for 2 questions? Yea, you got it!

Answer 1

This shape is a parallelogram.

A parallelogram has two sets of parallel, congruent sides that create the shape. Since segment BC is parallel to segment AD, this means that segment AD is congruent to segment BC.

Line AC bisects the parallelogram into two congruent triangles. The diagram shows that segments AB and CD are congruent to each other, and that angle BAC and angle DCA are congruent to each other. The bisecting line is AC, which is the hypotenuse that the two triangles share, making it congruent for both triangles.

One side, an included angle, and another side are congruent to each other. Using the SAS (side-angle-side) theorem, we can prove these angles to be congruent.

Answer 2

Hi there!

Segment AD is congruent to BC

Due to alternate interior angles being congruent if lines are parallel is what makes ∠BAC congruent to ∠DCA