8th grade Ch 7 L4

Determine whether each pair of polygons is similar. Explain. Are the two triangles shown similar?

• Yes, the triangles are similar. The sides are proportional: 3/5 = 4/12 = 5/13.

• No, the triangles are not similar. The sides are not proportional: 3/5 ≠ 4/12 ≠ 5/13.

• Yes, the triangles are similar. The angles are all equal, but the sides are not proportional.

• No, the triangles are not similar. The triangles have different shapes.

Are the two quadrilaterals shown similar? Explain your reasoning.

• Yes, the quadrilaterals are similar. The sides are proportional: 8/6 = 8/6 = 18/13.5 = 10/7.5 = 4/3.

• No, the quadrilaterals are not similar. The angles are not equal.

• No, the quadrilaterals are not similar. The sides are not proportional.

• Yes, the quadrilaterals are similar. All sides are equal.

The two triangles are similar. (Example 2) 3a. Determine the transformations that map one figure onto the other.

• A dilation centered at the origin with a scale factor equal to the ratio of corresponding sides.

• A translation followed by a reflection over the y-axis.

• A rotation of 90 degrees about the origin.

• A reflection over the x-axis followed by a translation.

The two triangles are similar. (Example 2) 3b. Find the missing side measures.

• x = 18, y = 2

• x = 12, y = 3

• x = 9, y = 4

• x = 6, y = 1

The two triangles are similar. (Example 2) 4a. Determine the transformations that map one figure onto the other.

• A dilation centered at the origin with a scale factor equal to the ratio of corresponding sides.

• A translation 5 units to the right.

• A rotation of 90 degrees about the origin.

• A reflection over the y-axis.

The two triangles are similar. (Example 2) 4b. Find the missing side measure. (Triangles with sides 5, x, 10 and 4.8, 8, 4)

• x = 8

• x = 6

• x = 10

• x = 4

How does the scale factor of a dilation relate to the ratio of two of the corresponding sides of the preimage and the image?

• The scale factor of a dilation is equal to the ratio of the lengths of any two corresponding sides of the preimage and the image.

• The scale factor of a dilation is equal to the sum of the lengths of any two corresponding sides of the preimage and the image.

• The scale factor of a dilation is equal to the difference between the lengths of any two corresponding sides of the preimage and the image.

• The scale factor of a dilation is equal to the product of the lengths of any two corresponding sides of the preimage and the image.

Determine whether each pair of polygons is similar. Choose the correct answer.

• Yes, the pairs of polygons are similar.

• No, the pairs of polygons are not similar.

• Only one pair of polygons is similar.

• The polygons are congruent, not similar.

Determine whether each pair of polygons is similar. Choose the correct answer.

• Yes, the pairs of polygons are similar.

• No, the pairs of polygons are not similar.

• Only one pair of polygons is similar.

• The polygons are congruent, not similar.

Each pair of polygons is similar. Determine the transformations that map one figure onto the other. Then find the missing side measures. (Example 2) 3. (Diagram: two parallelograms, one with sides 8, 12, 8, 12 and the other with sides x, 3, x, 3) What is the value of x?

• 2

• 4

• 6

• 12