Back to Prove theorems about parallelograms — Problem 1 · Task Set 11

Exercises: Prove Theorems About Parallelograms

Work through each section in order. Show all proof steps and justifications where indicated.

Grade 9·21 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-co-c-11

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Fluency Practice

$Parallelogram ABCD with diagonal AC drawn as a dashed line from top-left vertex A to bottom-right vertex C.$

Parallelogram $ABCD$ has diagonal $\overline{AC}$ drawn. To prove $\triangle ABC \cong \triangle CDA$ using ASA, a student uses the fact that $AB \parallel DC$ . Which angle pair does this parallel relationship justify as congruent?

$\angle BAC \cong \angle DCA$ (alternate interior angles, transversal $\overline{AC}$ , lines $AB \parallel DC$ )

$\angle ABC \cong \angle CDA$ (corresponding angles, transversal $\overline{AC}$ , lines $AB \parallel DC$ )

$\angle BAD \cong \angle BCD$ (alternate interior angles, transversal $\overline{AC}$ , lines $AB \parallel DC$ )

$\angle BAC \cong \angle DAC$ (alternate interior angles, transversal $\overline{AC}$ , lines $AB \parallel DC$ )