Scale and Similarity

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree.  How tall is the tree?

• 144 feet

• 72 feet

• 36 feet

Gwen scans a photo that is 4 in. wide by 6 in. tall into her computer. If she scales the height down to 3 in., how wide should the similar photo be?

• 3 in

• 2 in.

• 4 in

• 1 in

Pedro and his friends are visiting chocolate shops in Fairview. They take a cab from one chocolate shop to another. On a map, the two are separated by 3 centimeters. If the scale of the map is 1 centimeter = 2 kilometers, then what is the actual distance between the two chocolate shops?
____ = ____

•  

• 1.5 kilometers

• 6 kilometers

• 3 kilometers

What is the scale factor?

• 4

• 25

• 5

• 6

Triangle ABC is similar to triangle DEF. Which proportion can be used to find the length of DE in centimeters?

• 4/3 = DE/9

• 5/15 = DE/4

• 4/DE = 9/3

• 9/DE = 3/5

In similar figures JKLM and PQRS, the proportion (a)   must be true.

• QR/QP = JK/LM

• QR/KL = RS/JK

• QR/MJ = PQ/LM

• QR/KL = PS/JM

The dimensions of a triangle similar to triangle QRS are (a)   in centimeters.

• 8 cm, 14 cm, 17 cm

• 10 cm, 20 cm, 25 cm

• 4 cm, 10 cm, 13 cm

• 12 cm, 24 cm, 36 cm

Triangle ABC is similar to triangle FGH. The value of x in centimeters is (a)   .

• 22.5 cm

• 8 cm

• 10.8 cm

• 30 cm

Triangle RST is similar to triangle RVW. What is the value of d in millimeters?

• 27 mm

• 12 mm

• 9 mm

• 13 mm

Mr. Ortiz used similar triangles to make a design. Which statement about the triangles in the design must be true?

• They are the same size and shape.

• They are the same size but different shapes.

• They have corresponding angles that are congruent.

• They have corresponding sides that are congruent.