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 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. 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 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