Similarity and Scale Factor

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.

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

A student made a model of the Washington Monument using a scale in which 1 inch represents 15 feet. The actual height of the Washington Monument is approximately 555 feet. Which measurement is closest to the height of the model in inches?

• 37 in.

• 75 in.

• 46 in.

• 180 in.

Leon created a scale drawing of the school library in his art class. In the scale drawing, the length of the library is 13 inches. The length of the actual library is 78 feet. Which scale did Leon use to create the scale drawing of the school library?

• 1 inch represents 6 feet

• 1 inch represents \( \frac{1}{6} \) foot

• 6 inches represents 1 foot

• 6 inches represents \( \frac{1}{6} \) foot

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

A building has a height of 125 meters and a length of 80 meters. On a scale drawing of the building, the height is 25 centimeters. What is the length of the building on the scale drawing in centimeters?

• 55 cm

• 16 cm

• 20 cm

• 64 cm

In the scale used on a blueprint, $ \frac{1}{4} $ inch represents 2 feet. On the blueprint what is the length of a room with an actual length of 20 feet?

• 10 in.

• 5 in.

• $ \frac{1}{2} $ in.

• 2 $ \frac{1}{2} $ in.