Determining Similarity Using Ratios

Pick the correct Similarity Statement for the Triangles Shown.

• ΔABC ~ ΔXYZ

• ΔACB ~ ΔYZX

• ΔCAB ~ ΔZXY

• ΔABC ~ ΔZXY

Find the scale factor (common ratio) between the two triangles.

• 3/2

• 1

• 9/4

• 4/9

Determine if the two figures are similar or not using common ratios.

• Yes, because 6/4 = 8/6

• No, because 6/4 does not equal 8/6

• No, because 6/8 = 4/6

• Yes, because 6/8 = 4/6

Determine if the two figures are similar or not using common ratios.

• No, the ratios between corresponding sides are different.

• No, because the sides aren't equal.

• Yes, because all the ratios are 4 to 1

• Yes, because all the ratios are 8 to 1

If the sides of two similar triangles are in the ratio 2:3, and the perimeter of the smaller triangle is 18 cm, what is the perimeter of the larger triangle?

• 24 cm

• 27 cm

• 30 cm

• 36 cm

Two rectangles are similar. The first rectangle has sides of lengths 4 cm and 6 cm. If the second rectangle has a longer side of 9 cm, what is the length of its shorter side?

• 5.5 cm

• 6 cm

• 6.5 cm

• 7 cm

Two similar cylinders have heights in the ratio 3:5. If the volume of the smaller cylinder is 81 cubic units, what is the volume of the larger cylinder?

• 135 cubic units

• 225 cubic units

• 243 cubic units

• 405 cubic units

A 5 ft tall person casts a 10 ft shadow. At the same time, a nearby tree casts a 40 ft shadow. How tall is the tree?

• 10 ft

• 15 ft

• 20 ft

• 25 ft

A __________ is a comparison of two quantities.

• transformation

• scale

• ratio

• graph

Are the two figures similar? (check all ratios to see if they are equal)

• yes

• no