Grade 10 · Math · Geometry

10th grade Triangle similarity: AA, SSS and SAS worksheet

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Triangle similarity: AA, SSS and SAS

Grade 10 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Jun makes two triangle flags for a boat and wants △CDF ~ △QSU by SAS~. How long must QU be, in cm?
Kira plans two ramps for a toy car track and wants △GHY ~ △VWC by SAS~. How long must VC be, in cm?
Luz sketches a small and a big tent side and wants △QSU ~ △DFG by SAS~. How long must DG be, in cm?
Milo cuts two triangle sandwiches for a picnic and wants △VWY ~ △CDF by SAS~. How long must CF be, in cm?
5.
Noah compares two triangle pizza slices, △CDF and △QSU. Which statement is true?
- Congruent by SSS
- Not similar: the sides grow by 3, 4 and 5
- Similar by SSS~, scale factor 2/3
- Similar by SSS~, scale factor 3/2
6.
Pia compares two cheese wedges with triangle faces, △CDF and △QSU. Which statement is true?
- Similar by SSS~, scale factor 3/2
- Similar by SSS~: every side is 2 longer
- Not similar: 6/4 and 8/6 are different
- Congruent by SSS
7.
Ren compares two kite halves, △CDF and △QSU. Which statement is true?
- Not enough: the third sides are not given
- Similar by SAS~
- Congruent by SAS
- Similar by SSS~
8.
Tala compares two tent doors, △CDF and △QSU. Which statement is true?
- Not enough: side lengths are needed
- Congruent by AA
- Similar by AA: ∠F = 75° = ∠U
- Not similar: 65° and 75° do not match
Bo cuts a straight line GH across a triangle pizza slice. In △CDF, G is on CD, H is on CF, and GH ∥ DF. How long is DF, in inches?
Esme builds a ramp with a brace GH. In △CDF, G is on CD, H is on CF, and GH ∥ DF. How long is DF, in feet?

10th grade Triangle similarity: AA, SSS and SAS worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Similar triangles by AA, SSS and SAS. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can choose AA, SSS~ or SAS~, or say there is not enough to tell, from the marks on two triangles.
I can find the side that makes two triangles similar by SSS~ or SAS~, also when it is written with x.
I can find a missing side in a bowtie or a nested triangle, and describe the dilation and move that map one triangle onto the other.

Standard: G-SRT.A.3, G-SRT.B.5

Words to know

AA: Two pairs of equal angles: enough to make two triangles similar.

SSS~: All three pairs of sides share one scale factor.

SAS~: Two side ratios match, and the angle between those sides is equal.

included angle: The angle between two sides, at the corner where they meet.

bowtie: Two segments crossing at a point, with a parallel side at each end.

dilation: A move that makes a figure bigger or smaller by one scale factor.

Common mistakes

Your child called triangles similar by angle-angle with only one pair of equal angles.

Your child used SAS~ with an angle that is not between the two sides.

Your child thought more side lengths were needed when the facts given already prove similarity.

What to say

Ask: how many pairs of equal angles does AA need?

Ask: where must the equal angle sit for SAS~?

Ask: which rule, AA, SSS~ or SAS~, fits the facts you have?

Questions parents ask

What is the most common mistake with triangle similarity: aa, sss and sas?

Your child called triangles similar by angle-angle with only one pair of equal angles.

How can I help my child with triangle similarity: aa, sss and sas?

Ask: how many pairs of equal angles does AA need?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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