Grade 10 · Math · Geometry

10th grade Similar figures: corresponding sides, scale factor, and all circles are similar worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Similar figures: corresponding sides, scale factor, and all circles are similar

Grade 10 Math Worksheet

NameDate

Circle the best answer.

1.
Bo compares two tent fronts. △ABC has sides 8, 12, 18 and △DEF has sides 12, 18, 27. No angles are given. What proves they are similar?
- SSS~: 8/12, 12/18 and 18/27 are all 2/3
- AA: the angles must be equal, because the sides are in a ratio
- Not enough: the angles are needed too
- SAS~: two sides in a ratio and the angle between them
Read this first
Use this
Two triangles. AB = 6, DE = 4, AC = 9, DF = 6, and ∠A = ∠D = 55°. BC and EF are not given. Lengths in cm.
2.
Esme checks two sail triangles. AB/DE = AC/DF = 3/2 and ∠A = ∠D = 55°. The third sides are unknown. What proves they are similar?
- Not enough: the third pair of sides is needed
- SSS~: the three pairs of sides are in one ratio, including BC and EF
- AA: two pairs of equal angles
- SAS~: two sides in one ratio with the equal angle between them
3.
AC and DF are not given. Jun checks two map triangles. AB/DE = BC/EF = 3/2 and ∠A = ∠D = 55°. What can Jun conclude?
- SSS~: the three pairs of sides are in one ratio
- AA: two pairs of equal angles
- Not enough: the equal angle is not between the two proportional sides
- SAS~: two sides are in a ratio and an angle is equal, so the triangles are similar
4.
Given: AB/DE = AC/DF = 3/2. Nothing else is known. Kira knows AB/DE = AC/DF = 3/2 for two triangles. Which fact completes a proof of similarity by SAS~?
- ∠B = ∠E, an angle that is not between those sides
- ∠A = ∠D, the angle between AB and AC
- BC = EF, the third sides are equal
- AB = DE, the first sides are equal
Use this
Nothing else is known.
5.
Luz knows AB/DE = BC/EF = 2/3 for two triangles. Which fact completes a proof of similarity by SSS~?
- ∠A = ∠D, an angle that is not between AB and BC
- AC/DF = 2/3, so all three pairs of sides are in one ratio
- ∠C = ∠F, one more pair of equal angles
- AC = DF, so the third pair of sides is equal and all three match
6.
Milo knows ∠C = ∠F = 90° in two triangles. Which fact completes a proof of similarity by AA?
- AB = DE, the hypotenuses are equal
- AC/DF = 2, one pair of legs in a ratio
- ∠A = ∠D, a second pair of equal angles
- BC = EF, one pair of legs is equal
7.
Pia draws DE ∥ BC with D on AB and E on AC. AD = 4, DB = 6 and AE = 5. Which equation finds EC?
- 4/6 = DE/BC, using the parallel sides
- 4/10 = 5/EC, using the whole side AB
- 4/6 = EC/5, with the ratio turned over
- 4/6 = 5/EC, from AD/DB = AE/EC
8.
Ren marks D on AB and E on AC. AD = 3, DB = 6, AE = 4 and EC = 8. Is DE parallel to BC?
- Yes: AD/DB = AE/EC = 1/2, so DE ∥ BC by the converse
- Not enough: DE and BC are needed
- No: AD and AE are different lengths, so the lines cannot be parallel
- Yes: AD/AB = AE/EC
9.
Tala marks D on AB and E on AC. AD = 3, DB = 6, AE = 5 and EC = 8. Is DE parallel to BC?
- No: AD/DB = 1/2 but AE/EC = 5/8, so DE is not parallel to BC
- No: AD and AE are different lengths
- Yes: both ratios are close to one half, so the lines are close enough to parallel
- Yes: D and E lie on the sides of the triangle
10.
Zee draws DE ∥ BC with D on AB and E on AC. AD = 4, AB = 10 and AE = 6. Which equation finds AC?
- 4/6 = 6/AC, mixing AD, DB and AE
- 4/10 = AC/6, with the ratio turned over
- 4/10 = 6/AC, from AD/AB = AE/AC
- 4/10 = DE/6

10th grade Similar figures: corresponding sides, scale factor, and all circles are similar worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Similar figures and the scale factor. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can decide whether two figures are similar by AA, SAS~ or SSS~, and say what is missing when the facts are not enough.
I can use the triangle proportionality theorem and its converse, and set up similar triangles for a height or a distance I cannot measure.
I can say which dilation and rigid motions carry one figure onto a similar one, and why lengths grow by k, areas by k × k and volumes by k × k × k.

Standard: G-SRT.A.2, G-C.A.1

Words to know

similar (~): Same shape, maybe a different size: angles match and sides grow by one number.

similarity statement: △CDF ~ △UQS: letters in the same place go together (C with U, D with Q).

scale factor: The number every length is multiplied by, from the first figure to the second.

congruent: Same shape and same size: similar with scale factor 1.

circumference: The distance around a circle.

perimeter: The distance around a triangle: all three sides added.

dilation: A move that multiplies every distance from a center by the scale factor.

Common mistakes

Your child saw every side grow by the same amount and called the shapes similar. Similar sides grow by the same ratio, not the same amount.

Your child checked some pairs of sides and stopped.

Your child decided from the angles alone. Rectangles all have 90° angles, so the sides must also be in one ratio.

What to say

Ask: do all the pairs make the same ratio?

Questions parents ask

What is the most common mistake with similar figures: corresponding sides, scale factor, and all circles are similar?

Your child saw every side grow by the same amount and called the shapes similar. Similar sides grow by the same ratio, not the same amount.

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

See all Geometry

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records