Triangle and Angle Relationships

Lesson 14 of module two focuses on the angles of a triangle, specifically the angle sum theorem, which states that the interior angles of a triangle add up to 180 degrees. The lesson presents a third proof of this theorem using a quadrilateral divided into two congruent triangles. It also covers vocabulary related to angle relationships, including exterior and remote interior angles. Students engage in exercises to apply these concepts and present informal arguments. The lesson concludes with a summary and guidance on upcoming topics, including the Pythagorean theorem.

What is the sum of the interior angles of a triangle?

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

In the proof using a quadrilateral, what is the sum of the angles in the quadrilateral?

• 360 degrees

• 270 degrees

• 450 degrees

• 180 degrees

What is the relationship between alternate interior angles when a transversal cuts parallel lines?

• They are congruent

• They are supplementary

• They are equal to 90 degrees

• They are complementary

What do you call the angles inside a triangle that are not adjacent to a given exterior angle?

• Supplementary angles

• Adjacent angles

• Remote interior angles

• Alternate angles

How can you find the measure of an exterior angle of a triangle?

• By subtracting the adjacent interior angle from 180 degrees

• By adding all three interior angles

• By adding the two remote interior angles

• By subtracting the two remote interior angles

In exercise 5, what is the measure of angle X if the remote interior angles are 89 and 28 degrees?

• 117 degrees

• 139 degrees

• 101 degrees

• 180 degrees

What is the measure of angle X in exercise 6 if the interior angles are 69 and 111 degrees?

• 101 degrees

• 111 degrees

• 69 degrees

• 180 degrees

In exercise 7, if the exterior angle is 101 degrees, what is the sum of the remote interior angles?

• 139 degrees

• 101 degrees

• 79 degrees

• 180 degrees

In exercise 9, what is the measure of angle X if the remote interior angles are 107 and 32 degrees?

• 75 degrees

• 139 degrees

• 101 degrees

• 180 degrees

What is the measure of angle X in exercise 10 if the exterior angle is 156 degrees and one interior angle is 81 degrees?

• 75 degrees

• 24 degrees

• 156 degrees

• 180 degrees