Back to Use congruence and similarity to solve — Problem 1 · Task Set 18

Exercises: Apply Similarity and Congruence to Solve Problems

Work through each section in order. For proof problems, state the criterion used (SSS, SAS, ASA, AAS, AA, SAS~, SSS~) and identify CPCTC steps explicitly. Show all work for computation problems.

Grade 9·22 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-srt-b-5

Work through problems with immediate feedback

Fluency Practice

Apply congruence or similarity criteria directly. State the criterion used.

In parallelogram $ABCD$ , diagonal $\overline{AC}$ is drawn. You know $AB \parallel CD$ and $BC \parallel AD$ . Which criterion proves $\triangle ABC \cong \triangle CDA$ ?

SSA — two sides and a non-included angle

SAS — $AC = CA$ , $\angle BAC = \angle DCA$ , $\angle BCA = \angle DAC$

ASA — $\angle BAC \cong \angle DCA$ , $AC \cong CA$ , $\angle BCA \cong \angle DAC$

SSS — three pairs of congruent sides