Chapter 7: Congruence and Similarity

Determine if the two figures are congruent by using transformations. If so, explain the transformation or transformations that map the first figure onto the second figure.

• congruent; a clockwise rotation of 90 degrees followed by a translation

• congruent; a reflection followed by a translation

• congruent; translation

• not congruent

Write congruence statements comparing the corresponding parts in the congruent figures shown.

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Determine if the two figures are similar by using transformations.

• Similar; a reflection and a dilation map one figure onto the other

• Similar; a translation and a dilation map one figure onto the other

• Similar; a rotation and a dilation map one figure onto the other

• The figures are not similar

Find the value of x in the similar polygons above

• 3 ft

• 9 ft

• 15 ft

• 6 ft

The two triangles shown in the figure are similar. Find the distance d across the river.

• 81 meters

• 18 meters

• 16 meters

• 25 meters

Write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.

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The figures shown are similar. Find the perimeter of the second figure.

• 53.3 in.

• 30 in.

• 48 in.

• 32 in.

What does similar mean?

• resembling without being identical

• the exact same

• slightly the same

• congruent

What does congruent mean?

• the same number of sides

• identical in form

• different from each other

• same size

The figures shown are similar. Find the perimeter of the second figure.

• 18 cm

• 25 cm

• 20 cm

• 16 cm