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Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3.

Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3. 4. If the perimeter is 47, find x and the lengths of the three sides. Triangle Angles. Section 3.4.

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Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3.

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  1. Warm Up Classify each angle as acute, obtuse, or right. 1.2. 3. 4. If the perimeter is 47, find x and the lengths of the three sides.

  2. Triangle Angles Section 3.4

  3. Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.

  4. C A AB, BC, and AC are the sides of ABC. B A, B, C are the triangle's vertices.

  5. By Angle Measures Acute Triangle Three acute angles

  6. By Angle Measures Equiangular Triangle Three congruent acute angles

  7. By Angle Measures Right Triangle One right angle

  8. By Angle Measures Obtuse Triangle One obtuse angle

  9. Classify ABD by its angle measures. Example 1A: Classifying Triangles by Angle Measures Classify BDC by its angle measures.

  10. Example 1 Classify FHG by its angle measures.

  11. By Side Lengths Equilateral Triangle Three congruent sides

  12. By Side Lengths Isosceles Triangle At least two congruent sides

  13. By Side Lengths Scalene Triangle No congruent sides

  14. Remember! When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.

  15. Classify EHGby its side lengths. Example 2A: Classifying Triangles by Side Lengths Classify EHF by its side lengths.

  16. Example 2 Classify ACD by its side lengths.

  17. Example 3: Using Triangle Classification Find the side lengths of JKL.

  18. Example 3 Find the side lengths of equilateral FGH.

  19. Lesson Review Classify each triangle by its angles and sides. 1. MNQ 2.NQP 3. MNP 4. Find the side lengths of the triangle.

  20. Warm Up 1. Find the measure of exterior DBA of BCD, if mDBC = 30°, mC= 70°, and mD = 80°. 2. What is the complement of an angle with measure 17°? 3. How many lines can be drawn through N parallel to MP? Why?

  21. An auxiliary line is a line that is added to a figure to aid in a proof. An auxiliary line used in the Triangle Sum Theorem

  22. Example 1A: Application

  23. A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

  24. Example 2a The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

  25. Example 2: Finding Angle Measures in Right Triangles One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

  26. The interior is the set of all points inside the figure. The exterior is the set of all points outside the figure. 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. 4 is an exterior angle. Exterior Interior 3 is an interior angle.

  27. Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle. 4 is an exterior angle. The remote interior angles of 4 are 1 and 2. Exterior Interior 3 is an interior angle.

  28. Example 3: Applying the Exterior Angle Theorem Find mB.

  29. Example 3 Find mACD.

  30. Example 4 Find mP and mT.

  31. Example 4: Applying the Third Angles Theorem Find mK and mJ.

  32. 2 3 Lesson Review: Part I 1. The measure of one of the acute angles in a right triangle is 56 °. What is the measure of the other acute angle? 2. Find mABD. 3. Find mN and mP.

  33. Lesson Review: Part II 4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store?

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