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.
Exterior
Interior
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