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 - Challenge Me

NameDate

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

Kira wants two paper triangles similar by SSS~. What value of x makes the two triangles similar?
Milo wants two window panes similar by SSS~. What value of x makes the two triangles similar?
3.
Noah makes a kite design bigger and turns it: △CDF becomes △QSU, with CD matching QS. Which moves map △CDF onto △QSU?
- A dilation by 1/3, then a rotation
- A rotation only
- A dilation by 3, then a rotation
- Add 8 cm to each side, then a rotation
4.
Pia shrinks a paper triangle and flips it: △CDF becomes △QSU, with CD matching QS. Which moves map △CDF onto △QSU?
- A dilation by 2/5, then a reflection
- A reflection only
- A dilation by 5/2, then a reflection
- Take 6 cm off each side, then a reflection
5.
Ren enlarges a triangle on a map and slides it: △CDF becomes △QSU, with CD matching QS. Which moves map △CDF onto △QSU?
- A dilation by 2/3, then a translation
- A dilation by 3/2, then a translation
- Add 3 cm to each side, then a translation
- A translation only
6.
Tala shrinks a triangle sticker and turns it: △CDF becomes △QSU, with CD matching QS. Which moves map △CDF onto △QSU?
- A dilation by 4/3, then a rotation
- A rotation only
- A dilation by 3/4, then a rotation
- Take 2 cm off each side, then a rotation
Zee studies a folding chair from the side. CG and DF cross at Y, and CD ∥ GF. What is x?
Ari opens a pair of craft scissors. CG and DF cross at Y, and CD ∥ GF. What is x?
Bo looks at a folding table from the side. CG and DF cross at Y, and CD ∥ GF. What is x?
Esme maps two parallel streets crossed by two roads. CG and DF cross at Y, and CD ∥ GF. What is x?

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.

More geometry

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