Proportional Relationships in Similar Triangles

This lesson covers the properties of similar triangles, focusing on the proportional relationships of corresponding segments such as medians, angle bisectors, and altitudes. It explains how to solve for unknowns using these properties and introduces the triangle angle bisector theorem, which states that an angle bisector divides the opposite side into segments proportional to the other two sides.

What is the primary focus of lesson 7.5?

• Studying the properties of parallelograms

• Learning about quadratic equations

• Exploring proportional relationships in similar triangles

• Understanding circle theorems

How are the medians related in similar triangles?

• They bisect the angles of the triangles

• They are proportional to the corresponding sides

• They are equal in length

• They are perpendicular to each other

What is the value of X when the median on the left triangle is 20 and on the right is X, with sides 36 and 18 respectively?

• 10

• 5

• 15

• 20

In the context of similar triangles, how are angle bisectors used?

• To establish congruency between triangles

• To find proportional relationships between sides

• To determine the height of the triangles

• To calculate the area of the triangles

What is the value of X when the angle bisector on the left is 9 and on the right is 6, with sides 12 and X respectively?

• 6

• 7

• 8

• 9

How are altitudes used in the study of similar triangles?

• To determine the base lengths

• To identify the type of triangle

• To find proportional relationships between sides

• To calculate the perimeter of the triangles

What is the value of X when the altitude on the left is 3 and on the right is X, with sides 4 and 3 respectively?

• 3.5

• 4.75

• 5

• 2.25

According to the triangle angle bisector theorem, how are the segments of the opposite side affected?

• They are proportional to the lengths of the other two sides

• They are perpendicular to each other

• They are equal in length

• They are longer than the other two sides

What is the value of X when the side that the angle bisector intersects is cut into lengths 25 and X, with the other side being 28?

• 30

• 32

• 38

• 35

What is the value of N when the opposite side is 46.8, with segments N and 46.8 minus N, and the sides are 36 and 42 respectively?

• 23.6

• 24.8

• 22.4

• 25.2