Exploring Similar Polygons and Scale Factors

The video tutorial by Michael Phelps covers the concept of similar polygons, focusing on similarity ratios, congruent angles, and proportional sides. It explains the theorem on the perimeters of similar polygons and provides multiple examples involving trapezoids, triangles, and parallelograms to illustrate these concepts. The tutorial emphasizes the importance of using similarity statements to determine corresponding angles and sides, and demonstrates solving for unknown side lengths using proportions.

What is a similarity ratio?

• The ratio of the perimeters of two similar polygons

• The ratio of the areas of two similar polygons

• The ratio of the angles of two similar polygons

• The ratio of the lengths of the corresponding sides of similar polygons

Which of the following statements is true for similar polygons?

• Their corresponding sides are equal

• Their corresponding angles are proportional

• Their corresponding sides are congruent

• Their corresponding angles are congruent

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

In a similarity statement, what does the order of vertices indicate?

• The area of the polygons

• The corresponding vertices

• The type of polygons

• The size of the polygons

Tags

CCSS.HSG.SRT.A.2

What does the Perimeters of Similar Polygons Theorem state?

• The perimeters of two similar polygons are proportional to the angle ratio

• The perimeters of two similar polygons are equal

• The perimeters of two similar polygons are proportional to the scale factor between them

• The perimeters of two similar polygons are proportional to the area ratio

If trapezoid ABCD is similar to trapezoid EFGH, which angle in EFGH corresponds to angle B in ABCD?

• Angle H

• Angle G

• Angle F

• Angle E

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Given two similar triangles, if the ratio of their corresponding sides is 3:2, what is the ratio of their perimeters?

• 3:2

• 2:3

• 1:1

• 3:1

In similar polygons, if the measure of segment AB is 6 and the measure of segment EF is 3, what is the similarity ratio?

• 3:1

• 1:3

• 2:1

• 1:2

If the similarity ratio between two polygons is 4:3 and the perimeter of the smaller polygon is 60, what is the perimeter of the larger polygon?

• 90

• 75

• 45

• 80

Given two similar quadrilaterals, if the measure of segment AB is 8 and the measure of segment EF is 4, what is the measure of segment BC if the measure of segment FG is 6?

• 12

• 8

• 6

• 4

If the similarity ratio between two triangles is 5:3 and the perimeter of the larger triangle is 50, what is the perimeter of the smaller triangle?

• 25

• 30

• 20

• 15