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Congruence & Similarity (Set 3) Worksheet

Grade 8 Math · printable worksheet (PDF) with answer key · 14 problems · CCSS 8.G.A.4, 8.G.A.5

A printable grade 8 congruence & similarity (set 3) practice worksheet with 14 problems and a complete, step-by-step answer key — formatted to print cleanly on standard paper. Included in the one-time $20 unlock for the full NudgeLearn library.

Sample problems

Two figures are congruent when a sequence of rigid motions (translations, reflections, rotations) maps one onto the other: matching sides and angles are equal. Two figures are similar when one is a dilation (with optional rigid motions) of the other: matching angles are equal and matching sides are proportional. Find the scale factor, then set up a proportion to find each missing length. Keep answers exact.

1. Triangle $P QR$ is mapped onto triangle $S T U$ by a sequence of rigid motions, so the triangles are congruent. Side $P Q = 13$ cm matches side $S T$ . What is the length of $S T$ ?
2. The two rectangles are similar. What is the scale factor from the smaller rectangle to the larger one?
3. Two similar figures have matching sides of $18$ cm and $24$ cm. Write the scale factor from the smaller figure to the larger figure as a fraction in lowest terms.
4. Hexagon $H$ is similar to hexagon $K$ with a scale factor of $\frac{1}{3}$ from $H$ to $K$ . A side of $H$ measures $21$ cm. Find the matching side of $K$ .

Plus 10 more problems and a full answer key in the PDF.

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