Similar Triangles

Same shape, different size.

12 problems · about 21 minutes · G-SRT.A.3, G-SRT.B.5

What this lesson teaches

The student proves triangles similar and uses proportions to find missing lengths.

Straightforward practice. Get the method working first.

5 problems

Corresponding sides 5 and 20. What is the scale factor?
Answer 4
Why 4.
Why does AA prove similarity?
Answer The third angle follows, and equal angles fix the shape.
Why All three angles match, which fixes the shape at any size.
Corresponding sides 4 and 12. Scale factor?
Answer 3
Why 12 ÷ 4.
Scale factor 3 on a side of 7. Corresponding side?
Answer 21
Why 7 × 3.
How many equal angle pairs does AA need?
Answer 2
Why The third follows.

The same ideas with more to keep track of.

3 problems

Corresponding sides 10 and 5. Scale factor?
Answer 0.5
Why 5 ÷ 10.
A 3-4-5 triangle scaled to have shortest side 9. What is the longest side?
Answer 15
Why Factor 3.
Do similar figures have equal angles? 1 yes, 0 no.
Answer 1
Why Dilations preserve angles.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each criterion by whether it proves similarity or congruence.
Answer Similarity only: AA, Three proportional sides · Congruence: SSS with equal sides, SAS with equal sides
Why Equal is stronger than proportional.
Scale factor 2.5 on a side of 6. Corresponding side?
Answer 15
Why 6 × 2.5.
The Factor: Corresponding sides are 6 and 9. What is the scale factor?
Answer 1.5
Why 1.5.
The Missing Side: Scale factor 1.5 applied to a side of 8. What is the corresponding side?
Answer 12
Why 12.