Similar Figures Test – Grade 8 Math (Printable PDF)

Question 1 Dilate two points (2 points)

Dilate each point about the origin.

1. (−6, 9) with scale factor 1/3 (1 point)
2. (4, −5) with scale factor 3 (1 point)

Question 2 Dilate a triangle (3 points)

Triangle ABC is shown. It is dilated about the origin with scale factor 2.

1. Find the coordinates of A′, B′, and C′. (2 points)
2. Find the ratio A′B′ : AB. (1 point)

Question 3 Recover the factor (3 points)

A dilation about the origin sends A(4, 6) to A′(10, 15).

1. Find the scale factor. (1 point)
2. B is (−2, 8). Find B′. (1 point)
3. A side of the original figure is 8 units long. How long is the matching side of the image? (1 point)

Question 4 Congruent triangles (3 points)

The figure shows △JKL and △J′K′L′.

1. Describe a sequence of rigid motions that maps △JKL onto △J′K′L′. (2 points)
2. Are the triangles congruent? Give a reason. (1 point)

Question 5 Similar rectangles (3 points)

Rectangle P is 9 cm by 12 cm. Rectangle Q is 6 cm by 8 cm.

1. Are P and Q similar? Show your work. (2 points)
2. Find the ratio of the perimeter of P to the perimeter of Q. (1 point)

Question 6 Missing side (2 points)

Two triangles are similar. The first has sides 14, 21, and 28. The second has sides 10, 15, and x. Find x.

Question 7 Dilated segment (2 points)

Segment UV has endpoints U(4, 6) and V(−8, 2). It is dilated about the origin by a factor of 3/2.

1. Find U′ and V′. (1 point)
2. How does the length of U′V′ compare with the length of UV? (1 point)

Question 8 Toy car model (2 points)

A toy model of a car is built at a scale of 1 : 48. The model is 9 inches long. How long is the real car in feet?