Transcript Chapter 4
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