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4-1. Classifying Triangles. Holt Geometry. Warm Up. Lesson Presentation. Lesson Quiz. Do Now 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. right. acute. obtuse. x = 5; 8; 16; 23. Objectives.

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  1. 4-1 Classifying Triangles Holt Geometry Warm Up Lesson Presentation Lesson Quiz

  2. Do Now 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. right acute obtuse x = 5; 8; 16; 23

  3. Objectives Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths.

  4. Vocabulary acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

  5. 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.

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

  7. By Angle Measures Acute Triangle Three acute angles

  8. By Angle Measures Equiangular Triangle Three congruent acute angles

  9. By Angle Measures Right Triangle One right angle

  10. By Angle Measures Obtuse Triangle One obtuse angle

  11. Example 1: Classifying Triangles by Angle Measures Classify BDC by its angle measures. obtuse Classify ABD by its angle measures. acute

  12. Example 2 Classify FHG by its angle measures. equiangular

  13. By Side Lengths Equilateral Triangle Three congruent sides

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

  15. By Side Lengths Scalene Triangle No congruent sides

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

  17. Example 3: Classifying Triangles by Side Lengths Classify EHF by its side lengths. isosceles Classify EHGby its side lengths. scalene

  18. Example 4 Classify ACD by its side lengths. isosceles

  19. Example 5: Using Triangle Classification Find the side lengths of JKL. JK=KL=23.3 JL = 44.5

  20. Example 6 Find the side lengths of equilateral FGH. All = 17

  21. Example 7: Application A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam? 7

  22. 1 2 3 1 Activity #1 2 3 Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180˚.

  23. 1 1 2 3 3 2 Activity #2 (alternative) 1 2 3

  24. Y X Z Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. The smallest angle is opposite the shortest side while the largest angle is opposite the longest side.

  25. C B 2 5 5 12 B C 6 13 A A List the angles from smallest to largest:

  26. C C 2 9 3 11 B B 7 20 A A Can a triangle have the given lengths?

  27. C C 3 3 4 10 B B 8 11 A A Can a triangle have the given lengths?

  28. Describe possible lengths for the third side: 9, 12

  29. Describe possible lengths for the third side: 4, 15 3, 4

  30. Classify by Angles 60˚ 60˚ 60˚ Obtuse Acute Equiangular Right Classify by Sides Equilateral Isosceles Scalene

  31. x Classify by angles: Acute 67˚ 48˚

  32. z 70˚ Classify by angles: Right x y

  33. Obtuse / Scalene 5 2 Classify by angles and sides 120˚ 4 Right/ Isosceles Equiangular/ Equilateral

  34. Classify by angles and sides 125˚ Right / Scalene X

  35. A triangle with a 90˚ angle has sides that are 3 cm, 4 cm, and 5 cm long. Classify the triangle by its angles and sides. Right / Scalene

  36. y Classify by angles and sides: 70˚ 42˚ Acute / Scalene

  37. Classify by angles and sides: x 125˚ 160˚ Obtuse / Scalene

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