Free Printable AA, SAS, & SSS: proving triangles similar

1.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta PQR\sim\Delta TUV$ by $SAS\sim$

b)

$\Delta PQR\sim\Delta TUV$ by $AA\sim$

c)

$\Delta PQR\sim\Delta VUT$ by $SSS\sim$

d)

$\Delta PQR\sim\Delta VUT$ by $AA\sim$

2.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta PQR\sim\Delta RKL$ by $SAS\sim$

b)

$\Delta PQR\sim\Delta RKL$ by $AA\sim$

c)

$\Delta PQR\sim\Delta RLK$ by $SSS\sim$

d)

$\Delta PQR\sim\Delta RLK$ by $SAS\sim$

3.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta AHD\sim\Delta KTP$ by $SAS\sim$

b)

$\Delta AHD\sim\Delta PTK$ by $AA\sim$

c)

$\Delta AHD\sim\Delta KTP$ by $SSS\sim$

d)

$\Delta AHD\sim\Delta PKT$ by $AA\sim$

4.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta EFG\sim\Delta EML$ by $SAS\sim$

b)

$\Delta EFG\sim\Delta ELM$ by $SSS\sim$

c)

$\Delta EFG\sim\Delta EML$ by $SSS\sim$

d)

$\Delta EFG\sim\Delta EML$ by $AA\sim$

5.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta DEF\sim\Delta DRS$ by $SAS\sim$

b)

$\Delta DEF\sim\Delta RDS$ by $AA\sim$

c)

$\Delta DEF\sim\Delta DRS$ by $SSS\sim$

d)

$\Delta DEF\sim\Delta RDS$ by $AA\sim$

6.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta RST\sim\Delta RHG$ by $SAS\sim$

b)

$\Delta RST\sim\Delta RHG$ by $SSS\sim$

c)

$\Delta RST\sim\Delta GHR$ by $SAS\sim$

d)

$\Delta RST\sim\Delta RGH$ by $AA\sim$

7.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta LMN\sim\Delta LGF$ by $SAS\sim$

b)

$\Delta LMN\sim\Delta GLF$ by $AA\sim$

c)

$\Delta LMN\sim\Delta GLF$ by $SAS\sim$

d)

$\Delta LMN\sim\Delta LGF$ by $AA\sim$

8.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta JKL\sim\Delta JCD$ by $SAS\sim$

b)

$\Delta JKL\sim\Delta JDC$ by $SAS\sim$

c)

$\Delta JKL\sim\Delta DCJ$ by $SAS\sim$

d)

$\Delta JKL\sim\Delta CJD$ by $SAS\sim$

9.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta JKL\sim\Delta ABC$ by $SSS\sim$

b)

$\Delta JKL\sim\Delta BCA$ by $SSS\sim$

c)

$\Delta JKL\sim\Delta CAB$ by $SSS\sim$

d)

$\Delta JKL\sim\Delta BCA$ by $SSS\sim$

10.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta LMN\sim\Delta EFG$ by $SSS\sim$

b)

$\Delta LMN\sim\Delta EFG$ by $SAS\sim$

c)

$\Delta LMN\sim\Delta EFG$ by $AA\sim$

d)

$\Delta LMN\sim\Delta FEG$ by $SSS\sim$

11.

The triangles are similar. State the reason and complete the similarity statement.

a)

$\Delta JKL\sim\Delta EFG$ by $SSS\sim$

b)

$\Delta JKL\sim\Delta EFG$ by $SAS\sim$

c)

$\Delta JKL\sim\Delta FGE$ by $SSS\sim$

d)

$\Delta JKL\sim\Delta FEG$ by $AA\sim$

12.

Which of the following is a viable method of proving one triangle is similar to another?

a)

Show that 3 sides of one triangle are congruent to 3 sides of another.

b)

Show that 2 sides of one triangle & their included angle are congruent to 2 sides of another & their included angle.

c)

Show that 2 angles of one triangle are congruent to 2 angles of another.

d)

Show a sequence of rigid transformations (rotation, slide, reflection) map one triangle onto the other.

13.

Which of the following is a viable method of proving one triangle is similar to another?

a)

Show that 3 pairs of corresponding sides from one triangle to another have the same scale factor.

b)

Show that 2 sides of one triangle & their included angle are congruent to 2 sides of another & their included angle.

c)

Show that 2 angles of one triangle are similar to 2 angles of another.

d)

Show a sequence of rigid transformations (rotation, slide, reflection) map one triangle onto the other.

14.

Which of the following is a viable method of proving one triangle is similar to another?

a)

Show that 3 sides of one triangle are congruent to 3 sides of another.

b)

Show that 2 sides of one triangle & their included angle are congruent to 2 sides of another & their included angle.

c)

Show that 2 angles of one triangle are similar to 2 angles of another.

d)

Show a sequence of rigid transformations (rotation, slide, reflection), plus a dilation map one triangle onto the other.

15.

Which of the following is a viable method of proving one triangle is similar to another?

a)

Show that 3 sides of one triangle are congruent to 3 sides of another.

b)

Show that 2 sides of one triangle are proportional to 2 sides of another & their included angles are congruent.

c)

Show that 2 angles of one triangle are proportional to 2 angles of another.

d)

Show a sequence of rigid transformations (rotation, slide, reflection) map one triangle onto the other.

AA, SAS, & SSS: proving triangles similar

Total questions: 15

Worksheet time: 8mins

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