Similar Triangles

Same shape, different size.

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

NameDate

Figure — use these to answer the problems

Change the scale factor and watch both shapes. The angles hold while every length scales together.

Before: 4

After: 8

2 × 4 = 8

Original length4

Scale factor, top2

Scale factor, bottom1

Figure 1

Straightforward practice. Get the method working first.

5 problems

Corresponding sides 5 and 20. What is the scale factor?
Answer
2
Why does AA prove similarity?
- The third angle follows, and equal angles fix the shape.
- Because two angles determine the side lengths.
Corresponding sides 4 and 12. Scale factor?
Answer
Scale factor 3 on a side of 7. Corresponding side?
Answer
How many equal angle pairs does AA need?
Answer

The same ideas with more to keep track of.

3 problems

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

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.
Write each item under the heading it belongs to: AA · Three proportional sides · SSS with equal sides · SAS with equal sides
Similarity only
Congruence
Scale factor 2.5 on a side of 6. Corresponding side?
Answer
The Factor
Corresponding sides are 6 and 9. What is the scale factor?
Answer
The Missing Side
Scale factor 1.5 applied to a side of 8. What is the corresponding side?
Answer