Triangles and Similarity Checkpoint
A free Geometry lesson from the “Triangles, Similarity, and Trigonometry” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint blends congruence, similarity, scale factors, and right triangles. The goal is to decide whether the problem is about equal parts, proportional parts, or a right-triangle relationship. In Triangles, Similarity, and Trigonometry, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Use congruent triangle relationships
- Choose congruence shortcuts
- Use similarity and right-triangle tools
Worked example
Problem. Two similar triangles have matching sides 6 and 15. A smaller side is 8. Find the larger matching side.
- The scale factor is 15/6 = 2.5.
- Multiply 8 by 2.5.
- The larger side is 20.
- Connect the result back to Triangles and Similarity Checkpoint so the geometric relationship is explicit.
Answer: 20
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Triangles ABC and DEF are congruent. If AC = 18, what is DF?
Show solution
- AC corresponds to DF.
Answer: 18
2. Which shortcut uses two sides and the included angle?
Choices: SAS · SSA · AAA · AAS
Show solution
- Side-angle-side.
Answer: SAS
3. Which shortcut is not valid for general congruence?
Choices: SSA · SSS · SAS · ASA
Show solution
- SSA can be ambiguous.
Answer: SSA
4. A side of 7 scales by factor 4. What is the new length?
Show solution
- 7 x 4 = 28.
Answer: 28
5. Matching sides are 5 and 20. What is the scale factor from smaller to larger?
Show solution
- 20/5 = 4.
Answer: 4
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