Proportions of Similar Triangles

REVIEW Similarity, Triangle Proportions, Parallelograms

Use this to prepare for your TEST

Dilation

Compare corresponding sides to find the scale factor, k.

k=image/original

Multiple Choice

The green shape is a dilation (image) of the black shape. What is the scale factor of the dilation?

• 2

• 3

• 1/2

• 1/3

Fill in the Blanks

Center of Dilation

• Determines the position of the image. The center of dilation is NOT always (0,0)

• To Find Center of Dilation: extend a line thru the corresponding vertices of the shape

• The CENTER OF DILATION is where the lines INTERSECT

Multiple Choice

The segment AB is dilated to create the segment A'B' . Find the center of dilation.

• (5, 7)

• (-1, 4)

• (-4, 1)

• (-2, 3)

Multiple Choice

Triangle DEF is dilated to form triangle D'E'F' find the center of dilation.

• (0, 0)

• (-1, 4)

• (7, 3)

• (9, 1)

Multiple Choice

Rectangle ABCD has been dilated to form A'B'C'D'. Find the center of dilation

• (0, 0)

• (4, 2)

• (2, 4)

• (4, -1)

Multiple Choice

Find the center of dilation

• (0, 0)

• (2, 2)

• (3, 3)

• (0, 3)

Proving Triangles Similar

• similar shapes have CONGRUENT corresponding angles

• all corresponding sides have the SAME scale factor (sides are proportional

Multiple Choice

If the triangles are similar, why?

• AA∼

• SSS∼

• SAS∼

• Not similar

Multiple Choice

If the triangles are similar, why?

• AA∼

• SSS∼

• SAS∼

• Not similar

Remember Vertical Angles are always CONGRUENT

vertical angles are not usually marked congruent in drawings but can be helpful to prove AA, or SAS depending on what information is given--REMEMBER sides have to have same scale factor!

The triangles are only similar if all the ratios (fractions) are equal!

Multiple Choice

Find the missing side, PR

• 10.5

• 13

• 13.5

• 11

Multiple Choice

Do the ratios 1/2

and 13/16

form a proportion?

• Yes, the fractions are equal

• No, the fractions are not equal

Multiple Choice

Which statement is true?

• The triangles are similar by SAS∼

  because

  5/23 = 12/59.8

• The triangles are NOT similar

  because

  5/23 ≠ 12/59.8

Multiple Choice

Are these triangles similar?

• Yes

• No

Fill in the Blanks

Multiple Choice

The triangles are similar. Use triangle proportions to solve for the missing length.

• 7.2

• 144

• 45

• 8.9

Triangle Proportions

If the similar triangles have parallel lines, then the corresponding parts are proportional.

15/6 = 25/x

solve by cross multiplying!

Multiple Choice

Which proportion is set up correctly?

• 30/25 = x/(77-x)

• 30/25 = x/77

• 30/25 = 77/x

• 30/25 = (77-x)/x

Multiple Choice

Solve for the missing side.

• 1.5

• 5

• 2.5

• 3

Properties Parallelograms

opp angles congruent

same side angle pairs SUM to 180

diagonals bisect one another.

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