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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.

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Chapter 4

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  1. Chapter 4 4-3 Angle Relationship in triangles

  2. SAT Problem of the day

  3. solution Right Answer: A

  4. Objectives Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles.

  5. 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

  6. What is an auxiliary line? • An auxiliary line is a line that is added to a figure to aid in a proof.

  7. Example#1 • Use the diagram drawn below to find mXYZ

  8. Example#2 • Use the diagram drawn below to find mYWZ.

  9. Example#3 • Use the diagram to find mMJK.

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

  11. 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.

  12. Example#4 • One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

  13. 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?

  14. Student guided practice • Do problems 6 to 8 in your book page 235

  15. 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

  16. 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

  17. 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.

  18. Exterior angle theorem

  19. Example#6 • Find mB.

  20. Example#7 • Find mACD.

  21. Student guided practice • Do problems 9 and 10 in your book page 235

  22. Third angle theorem

  23. Example#8 • Find mK and mJ

  24. Example#9 • Find mP and mT.

  25. Student Guided practice • Do problems 12 and 13 in your book page 235

  26. Homework!!! • Do problems 16-22 in your book page 236

  27. Closure • Today we learned about angles of triangles • Next class we are going to learn about congruent triangles

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