Similarity Exam Practice

What does it mean to be similar shapes?

• Different shape but same size

• Same shape but not the same size

• Same size and same shape

• Different shape and different size

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

What does it mean to be corresponding sides?

• The sides are parallel.

• They have congruent angles.

• They match positions on the two shapes.

• They are the same length.

Tags

CCSS.8.G.A.2

Which side corresponds with side AB?

• SP (green)

• PQ (orange)

• QR (red)

• SR (blue)

Tags

CCSS.8.G.A.2

Which part of similar shapes are always equal? (Choose 2)

• Length of corresponding sides

• Measure of corresponding angles

• Ratio of the corresponding sides

• The area inside the shape

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Two triangles are similar and the ratio of their corresponding sides is 3:5. If one side of the smaller triangle is 6 cm, what is the length of the corresponding side in the larger triangle?

• 8 cm

• 15 cm

• 20 cm

• 10 cm

Answer explanation

Use the base ratio (3:5) to create a proportion using the small side (6) and the large side (x).

The following triangles are similar. The corresponding side lengths are 6 cm, 8 cm, and 10 cm, and side lengths 9 cm, 12 cm, and x cm.

Which proportion can be used to solve for x?

• 6/8 = 9/x

• 6/9 = 12/8

• 6/10 = 9/x

• x/9 = 6/9

Answer explanation

The proportion does not matter as long as the two proportions correspond with each other.

Example: One shape has sides 1, 2, and 3.

The other shape has sides 11, 22, and 33.

The following proportions would match:

1/2 = 11/22 or 1/11 = 2/22

The following would NOT match:

1/2 = 22/33 or 1/11 = 22/2

Tags

CCSS.HSG.SRT.A.2

Prove that the two triangles are similar: Triangle PQR with side lengths 4 cm, 6 cm, and 8 cm, and Triangle STU with side lengths 6 cm, 9 cm, and 12 cm.

• The triangles are similar because their corresponding sides are in proportion:

  4/6 = 2/3,

  6/9 = 2/3,

  and 8/12 = 2/3.

• The triangles are not similar because their side lengths are different.

• The triangles are similar because they probably have the same angles.

• The triangles are similar because they like the same movies.

Tags

CCSS.HSG.SRT.A.2

Explain the angle-angle (AA) postulate for proving similarity of triangles.

• If two sides of one triangle are equal to two angles of another triangle, then the two triangles are similar.

• If two angles of one triangle are equal to two sides of another triangle, then the two triangles are similar.

• If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

• If two angles of a triangle add up to 180 then the triangle is not a triangle.

Tags

CCSS.HSG.SRT.B.5

If two triangles are similar and angle A is 40 degrees, what is the measure of the angle that corresponds to angle A?

• 80 degrees

• 90 degrees

• 40 degrees

• 30 degrees

Tags

CCSS.HSG.SRT.A.2

• Larger, multiply it by 2

• Smaller, multiply it by 2

• Larger, divide it by 2

• Smaller, divide it by 2

Tags

CCSS.8.G.A.3