Similarity, Dilations, and Volume Review

Similarity, Dilations, and Volume Review

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Volume

• Identify the shape

• Use the correct formula

• r: radius (remember to divide by 2 if they give you the diameter)

• h: height

• B: area of the base (you have to find this separately first)

Multiple Choice

Find the volume of the cone. Round your answers to the nearest tenth.

• 320.4 in³

• 314.2 in³

• 205.5 in³

• 267.4 in³

Dilations

• ABC is the pre-image (original)

• A'B'C' is the image (after the dilation)

• The figure gets bigger or smaller, based on a scale factor.

• To find coordinates, multiply the original coordinate by the scale factor

• Scale factor >1: enlargement

• Scale factor <1: reduction

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)
• A'(6,6) B'(9,9) C'(12,6)
• A'(0,0) B'(3,3) C'(6,0)
• A'(1,1) B'(2,2) C'(3,1)

Triangle Similarity

• SSS: All pairs of corresponding sides are proportional (you set up the fractions and they all simplify to the same thing)

• Remember to pair largest side with largest side and smallest side with smallest side

• SAS: Two pairs of sides are proportional, and the angle IN BETWEEN them is congruent

• AA: Two pairs of angles are congruent (meaning equal)

• Remember you can add vertical angles

• Also look for possible shared angles that would be congruent.

Multiple Choice

State if the triangles in each pair are similar. If so, state how you know they are similar.

• Yes, AA Similarity

• Yes, SSS Similarity

• Yes, SAS Similarity

• Not Similar

Using Similarity to Find Missing Sides

• Pair up the sides that "go together"

• Set up a proportional equation

• Cross-multiply to solve for x

Multiple Choice

The two right triangles below are similar. What is x, the missing side length in triangle DEF? 

• 3.75
• 9.75
• 10
• 12