Exploring Similar Figures and Proportions

What does it mean for two figures to be similar?

• Their angles are congruent and their perimeters are equal.

• Their sides are equal and their areas are equal.

• Their angles are congruent and their sides are proportional.

• Their angles are congruent and their sides are equal.

In similar triangles, if side AB corresponds to side FG, what should be true about their ratios?

• AB/FG should be equal to FG/AB.

• AB/FG should be equal to AC/FH.

• AB/FG should be equal to AB/BC.

• AB/FG should be equal to BC/GH.

When setting up a proportion to solve for a missing side, what is important to remember?

• The ratios must be set up with the larger triangle's sides in the denominator.

• The ratios must be consistent with corresponding sides.

• The ratios must be set up with the smaller triangle's sides in the numerator.

• The ratios must be set up with the larger triangle's sides in the numerator.

If 12/8 = 9/X, what is the value of X?

• 9

• 12

• 8

• 6

In the second example, if X corresponds to 7 and 14 corresponds to 6, what is the value of X?

• 14

• 6

• 7

• 16.3

For parallelograms, if 10/2 = 6/X, what is the value of X?

• 2

• 3

• 5

• 1.2

In the nested rectangles example, if the top of the smaller rectangle is X and the top of the larger rectangle is 12, what is the value of X?

• 7.5

• 12

• 8

• 5

In the story problem, if a 36-inch yardstick casts a 21-inch shadow, what is the height of a building that casts a 168-foot shadow?

• 21 feet

• 36 feet

• 168 feet

• 3024 feet

What is the first step in solving the story problem involving the yardstick and the building?

• Calculate the shadow length of the building.

• Draw a picture of the yardstick and the building.

• Set up a proportion comparing the yardstick and the building.

• Measure the height of the building.

After setting up the proportion 168/21 = X/36, what is the next step?

• Divide the numerators.

• Add the numerators.

• Cross multiply.

• Subtract the denominators.