Similar figures: corresponding sides, scale factor, and all circles are similar
Grade 10 Math Worksheet
Circle the best answer.
No side lengths are given. Ari plans two triangle sails. In △ABC and △DEF, ∠A = ∠D = 50° and ∠B = ∠E = 60°. What proves they are similar?
- Not enough: a side length is needed
- SAS~: two sides in a ratio and the angle between them
- SSS~: the three pairs of sides are in one ratio
- AA: two pairs of equal angles are enough
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?
- SAS~: two sides in a ratio and the angle between them
- AA: the angles must be equal, because the sides are in a ratio
- SSS~: 8/12, 12/18 and 18/27 are all 2/3
- Not enough: the angles are needed too
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Two triangles. AB = 6, DE = 4, AC = 9, DF = 6, and ∠A = ∠D = 55°. BC and EF are not given. Lengths in cm.
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?
- SSS~: the three pairs of sides are in one ratio, including BC and EF
- AA: two pairs of equal angles
- Not enough: the third pair of sides is needed
- SAS~: two sides in one ratio with the equal angle between them
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?
- SAS~: two sides are in a ratio and an angle is equal, so the triangles are similar
- SSS~: the three pairs of sides are in one ratio
- Not enough: the equal angle is not between the two proportional sides
- AA: two pairs of equal angles
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
- AB = DE, the first sides are equal
- BC = EF, the third sides are equal
- ∠A = ∠D, the angle between AB and AC
Use this
Nothing else is known.
Luz knows AB/DE = BC/EF = 2/3 for two triangles. Which fact completes a proof of similarity by SSS~?
- ∠C = ∠F, one more pair of equal angles
- ∠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
- AC = DF, so the third pair of sides is equal and all three match
Milo knows ∠C = ∠F = 90° in two triangles. Which fact completes a proof of similarity by AA?
- ∠A = ∠D, a second pair of equal angles
- AC/DF = 2, one pair of legs in a ratio
- BC = EF, one pair of legs is equal
- AB = DE, the hypotenuses are equal
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/AB = AE/EC
- Not enough: DE and BC are needed
- No: AD and AE are different lengths, so the lines cannot be parallel
- Yes: AD/DB = AE/EC = 1/2, so DE ∥ BC by the converse
Tala marks D on AB and E on AC. AD = 3, DB = 6, AE = 5 and EC = 8. Is DE parallel to BC?
- Yes: D and E lie on the sides of the triangle
- No: AD/DB = 1/2 but AE/EC = 5/8, so DE is not parallel to BC
- Yes: both ratios are close to one half, so the lines are close enough to parallel
- No: AD and AE are different lengths
Zee draws DE ∥ BC with D on AB and E on AC. AD = 4, AB = 10 and AE = 6. Which equation finds AC?
- 4/10 = DE/6
- 4/6 = 6/AC, mixing AD, DB and AE
- 4/10 = 6/AC, from AD/AB = AE/AC
- 4/10 = AC/6, with the ratio turned over