CHAPTER 4 4-3 Angle Relationship in triangles

SAT Problem of the day

solutionRight Answer: A

ObjectivesFind 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 mXYZ

Example#2◦Use the diagram drawn below to find mYWZ.

Example#3◦Use the diagram to find mMJK.

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 mB.

Example#7◦ Find mACD.

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

Third angle theorem

Example#8◦ Find mK and mJ

Example#9◦ Find mP and mT.

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