Proportions and Similarity in Geometry

This video tutorial explains the concept of similar polygons, focusing on triangles and trapezoids. It demonstrates how to determine similarity by comparing corresponding angles and side lengths, using proportions. The tutorial provides examples with triangles and trapezoids, showing how to calculate and verify similarity through proportional relationships.

What must be true for two polygons to be considered similar?

• Their corresponding angles must be equal.

• They must have the same perimeter.

• Their corresponding angles and side lengths must be proportional.

• They must have the same area.

When comparing two triangles, what is the first step to determine if they are similar?

• Check if they have the same perimeter.

• Check if they have the same area.

• Compare their angles.

• Create a ratio or proportion of their corresponding sides.

If the bottom side of triangle one is 3 and triangle two is 9, what is the proportion?

• 2:3

• 3:9

• 1:3

• 1:2

What is the proportion of the left leg of triangle one (4) to triangle two (12)?

• 1:2

• 1:3

• 3:4

• 2:3

If the hypotenuse of triangle one is 5 and triangle two is 15, what is the proportion?

• 1:3

• 1:2

• 3:4

• 2:3

What can you conclude if two triangles have side lengths in the ratio 1:3?

• They are congruent.

• They are similar.

• They have the same perimeter.

• They have the same area.

What is the proportion of the small base of trapezoid A (5) to trapezoid B (10)?

• 1:2

• 1:3

• 2:3

• 3:4

If trapezoids A and B are similar, what can be said about their side lengths?

• They are in a 1:2 proportion.

• They are in a 3:4 proportion.

• They are equal.

• They are in a 2:3 proportion.

What is the value of y if the leg of trapezoid A is 6 and trapezoid B is y, given a 1:2 proportion?

• 14

• 12

• 10

• 6

What is the value of z if the larger base of trapezoid A is 9 and trapezoid B is z, given a 1:2 proportion?

• 18

• 16

• 22

• 20