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Back to Use congruence and similarity to solve — Problem 2 · 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
A

Fluency Practice

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

1.

In rectangle ABCDABCD, AB‾≅DC‾\overline{AB} \cong \overline{DC}, BC‾≅BC‾\overline{BC} \cong \overline{BC} (reflexive), and ∠ABC≅∠DCB\angle ABC \cong \angle DCB (both right angles). A student concludes: "By CPCTC, AC‾≅DB‾\overline{AC} \cong \overline{DB}." Identify the missing step and state the complete proof.