CHAPTER 4

4-3 Angle Relationship in triangles

SAT Problem of the day

solution Right Answer: A

Objectives Find the measures of interior and exterior angles of triangles.

Apply theorems about the interior and exterior angles of triangles.

sum of the interior angles of a triangle ◦ Do you know what is an interior angle of a triangle?

◦ Answer: They are the angles in the inside of a triangle ◦ Do you know what is an exterior angle of a triangle?

◦ Answer: they are the angles form in the outside of a triangle ◦ Who much do all the interior angles of a triangle add up?

◦ Answer: they add up to 180 degrees

What is an auxiliary line?

◦ An auxiliary line is a line that is added to a figure to aid in a proof.

Example#1 ◦

Use the diagram drawn below to find m



XYZ

Example#2 ◦

Use the diagram drawn below to find m



YWZ.

Example#3 ◦

Use the diagram to find m



MJK.

Student guided practice ◦ DO problems 1- 4 in the worksheet and 4 and 5 in your book page 235

What is a corollary?

◦ A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

Example#4 ◦

One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

Example#5 ◦

The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

Student guided practice ◦ Do problems 6 to 8 in your book page 235

Angle relationship ◦ The interior is the set of all points inside the figure. The exterior is the set of all points outside the figure. Interior Exterior

Angle relationship ◦ An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side.

Interior angle <3 and exterior angle <4

Angle relationship ◦ Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle.

◦ The remote interior angles of  4 are  1 and  2.

Exterior angle theorem

Example#6 ◦

Find m



B.

Example#7 ◦

Find m



ACD.

Student guided practice ◦ Do problems 9 and 10 in your book page 235

Third angle theorem

Example#8 ◦

Find m



K and m



J

Example#9 ◦

Find m



P and m



T.

Student Guided practice ◦ Do problems 12 and 13 in your book page 235

Homework!!!

◦ Do problems 16-22 in your book page 236

Closure ◦ Today we learned about angles of triangles ◦ Next class we are going to learn about congruent triangles