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Geometry

5-1 Classifying Triangles. Geometry. Today we will be learning how to classify triangles according to length of sides and measurement of the angles. First we will learn to classify by the . ANGLES. Right triangles have ONE right angle. Acute Triangles have three acute angles.

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Geometry

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  1. 5-1 Classifying Triangles Geometry

  2. Today we will be learning how to classify triangles according to lengthofsides and measurement of the angles.

  3. First we will learn to classify by the ANGLES

  4. Right triangles have ONE right angle

  5. Acute Triangles have threeacute angles Smaller than 90o Smaller than 90o Acute Angle Smaller than 90o

  6. Obtuse Triangles have ONEobtuse angle Obtuse Angle

  7. We will now learn to classify triangles by their sides.

  8. Equilateral Triangles have 3 equal sides If you collapsed all of the sides they would form a line.

  9. Isosceles Triangles have 2 equal sides.

  10. Scalene Triangles have NO equal sides.

  11. Classifying Triangles by Their Sides • EQUILATERAL – 3 congruent sides • ISOSCELES – at least two sides congruent • SCALENE – no sides congruent EQUILATERAL ISOSCELES SCALENE

  12. Classifying Triangles by Their Angles • EQUIANGULAR – all angles are congruent • ACUTE – all angles are acute • RIGHT – one right angle • OBTUSE – one obtuse angle ACUTE EQUIANGULAR RIGHT OBTUSE

  13. Can You Classify the Different Triangles in the Picture Below? Classify the following triangles: AED, ABC, ACD, ACE • Triangle AED = Equilateral, Equiangular • Triangle ABC = Equilateral, Equiangular • Triangle ACD = Isosceles, Obtuse • Triangle ACE = Scalene, Right

  14. 1-1a

  15. 1-3a Slide 3 of 3

  16. 1-3b Slide 3 of 3

  17. 1-3c Slide 3 of 3

  18. 1-3d Slide 3 of 3

  19. You have now learned that triangles can be classified by either their sides or their angles.

  20. 5-2 Angles of a Triangle

  21. 1-1a Slide 1 of 2

  22. 1-2a Slide 2 of 2

  23. 1-2b Slide 2 of 2

  24. 1-2c Slide 2 of 2

  25. 1-2d Slide 2 of 2

  26. 1-2d Slide 2 of 2

  27. 1-2e Slide 2 of 2

  28. 1-2e Slide 2 of 2

  29. 1-2f Slide 2 of 2

  30. 1-2g Slide 2 of 2

  31. 1-2h Slide 2 of 2

  32. 1-2i Slide 2 of 2

  33. 1-2j Slide 2 of 2

  34. 1-2j Slide 2 of 2

  35. Findm∠ JKM. STEP1 Write and solve an equation to find the value of x. (2x – 5)° = 70°+ x° x = 75 STEP2 Substitute 75 for xin 2x–5 to find m∠ JKM. 2x–5 = 75 –5 = 2 145 ANSWER The measure of∠ JKMis145°. EXAMPLE 3 Find an angle measure SOLUTION Apply the Exterior Angle Theorem. Solve for x.

  36. Find the measure of 1 in the diagram shown. The measure of∠ 1in the diagram is 65°. ANSWER for Examples 3 and 4 GUIDED PRACTICE

  37. Find the measure of each interior angle of ABC, where mA=x , mB=2x°, and mC=3x°. ° x 180° A + B + C = x + 2x + 3x = 180° 6x = 180° 2x 3x x = 30° 2x = 2(30) = 60° B = 3(30) = 90° C = 3x = for Examples 3 and 4 GUIDED PRACTICE SOLUTION

  38. Find the measures of the acute angles of the right triangle in the diagram shown. ANSWER 26° and 64° for Examples 3 and 4 GUIDED PRACTICE

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