Exploring T Angles in Unit 6

What does the Triangle Proportionality Theorem state?

• If a line is parallel to one side of a triangle, it divides the other two sides proportionally.

• If a line bisects an angle of a triangle, it divides the opposite side proportionally.

• If a triangle has two equal sides, it is an isosceles triangle.

• If a triangle has three equal sides, it is an equilateral triangle.

What is the converse of the Triangle Proportionality Theorem?

• If a line divides two sides of a triangle proportionally, it is parallel to the third side.

• If a triangle has three equal sides, it is an equilateral triangle.

• If a line bisects an angle of a triangle, it divides the opposite side proportionally.

• If a triangle has two equal sides, it is an isosceles triangle.

In the example where 14/12 = x/15, what is the value of x?

• 12

• 17.5

• 14

• 15

In the example where 10/45 = x/36, what is the value of x?

• 45

• 10

• 8

• 36

In the example where 30/(x+7) = 25/15, what is the value of x?

• 7

• 25

• 11

• 15

What does the Triangle Angle Bisector Theorem state?

• If a triangle has three equal sides, it is an equilateral triangle.

• If a line is parallel to one side of a triangle, it divides the other two sides proportionally.

• An angle bisector in a triangle separates the opposite sides into two segments that are proportional to the lengths of the other two sides.

• If a triangle has two equal sides, it is an isosceles triangle.

In the example where 4.8/x = 12/18, what is the value of x?

• 7.2

• 18

• 12

• 4.8

In the example where 15/24 = x/36, what is the value of x?

• 24

• 22.5

• 36

• 15

Which theorem states that if a line is parallel to one side of a triangle, it divides the other two sides proportionally?

• Triangle Angle Bisector Theorem

• Pythagorean Theorem

• Isosceles Triangle Theorem

• Triangle Proportionality Theorem

Which theorem involves an angle bisector dividing the opposite side into segments proportional to the other two sides?

• Pythagorean Theorem

• Triangle Angle Bisector Theorem

• Triangle Proportionality Theorem

• Isosceles Triangle Theorem