Question

1. given: parallelogram abcd shown below, diagonals \\(\overline{ac}\\) and \\(\overline{bd}\\) intersect at e

prove: \\(\angle acd \cong \angle cab\\)
① abcd is a parallelogram ① given
② \\(\overline{ab} \parallel \overline{cd}\\) & \\(\overline{ab} \cong \overline{cd}\\) ② parallelogram \\(\
ightarrow\\) opp.sides \\(\cong\\) & \\(\parallel\\)
③

Explanation:

Step1: State given information

ABCD is a parallelogram (Given)

Step2: Use parallelogram property

$\overline{AB} \parallel \overline{CD}$ (Opposite sides of parallelogram are parallel)

Step3: Identify alternate interior angles

$\angle ACD$ and $\angle CAB$ are alternate interior angles formed by transversal $\overline{AC}$ cutting parallel lines $\overline{AB}$ and $\overline{CD}$. Alternate interior angles are congruent.
$\angle ACD \cong \angle CAB$

Answer:

$\boldsymbol{\angle ACD \cong \angle CAB}$ is proven using the alternate interior angles theorem for parallel sides of a parallelogram.