1. UNIT 4: TRIANGLE CONGRUENCE 4.1 Classifying Triangles

2. 2.3. right acute obtuse x = 5 2x + 6 + x + 3 + 3x + 8 = 47 6x + 17 = 47 6x = 30 2x + 6 2(5) + 6 10 + 6 16 Warm Up 11/15 (HW #18 [4.1] Pgs 219 – 220 #s 12 – 18, 23 – 28) Classify each angle as acute, obtuse, or right. 1. 2. 4. If the perimeter is 47, find x and the lengths of the three sides. 3x + 8 3(5) + 8 15 + 8 23 x + 3 5 + 3 8 – 17 –17 6

3. Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths. Objectives (see page 216) *Standard 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems

4. B A C 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. AB, BC, and AC are the sides of ABC.  A,  B, and  C are the angles of ABC. *see page 216

5. Acute Triangle Triangle Classification By Angle Measures Acute Triangle Right Triangle Obtuse TriangleEquiangular Triangle *all angles are acute *has ONE right angle *has ONE obtuse angle *all angles are congruent *see page 216

6. Check It Out! Example 1 (see page 216) Classify EFH by its angle measures. Classify FHG by its angle measures. Classify EHG by its angle measures. m  HFG = 60° m  FGH = 60° m  FHG = 60° m  HEF = 30° (acute  ) m  FHE = 30° (acute  ) m  EFH = 120° (obtuse  ) m  EHG = 90° (right  ) m  HGE = 60° (acute  ) m  HEG = 30° (acute  ) Equiangular Triangle Obtuse Triangle Right Triangle

7. 1. Classify BDC by its angle measures. Example 1A: Classifying Triangles by Angle Measures (see page 216) 2. Classify ABD by its angle measures. 3. Classify ADC by its angle measures. m  BAD = 80° (acute  ) m  ADB = 20° (acute  ) m  DBA = 80° (acute  ) m  DBC = 100° (obtuse  ) m  BCD = 10° (acute  ) m  BEFH = 70° (acute  ) m  ADC = 90° (right  ) m  DAC = 80° (acute  ) m  C = 10° (acute  ) Right Triangle Acute Triangle Obtuse Triangle

8. Equilateral Triangle Triangle Classification By Side Lengths Equilateral Triangle Isosceles Triangle Scalene Triangle *all sides equal *two sides equal *no sides equal *see page 217

9. Classify ACD by its side lengths. Check It Out! Example 2 (see page 217) Classify ABC by its side lengths. AD = 18 CD = 5 AC = 15 Scalene AB = 15 BC = 15 AC = 15 Equilateral

10. Example 2A: Classifying Triangles by Side Lengths (see page 217) 4. Classify EHF by its side lengths. 5. Classify EGH by its side lengths. EH = 12 EF = 10 HF = 10 EH = 12 EG = 14 HG = 11 Isosceles Scalene

11. Find the side lengths of equilateral FGH. Check It Out! Example 3 (see page 217) Step 1 Find the value of y. Step 2 Substitute y into the expressions to find the side lengths. FG = GH 3y – 4 = 2y + 3 – 2y –2y + 4 3y = 2y + 7 y = 7 FG = 3y – 4 FG = 3(7) – 4 FG = 21 – 4 FG = 17 GH = 2y + 3 GH = 2(7) + 3 GH = 14 + 3 GH = 17FH = 17 FH = 5y – 18 FH = 5(7) – 18 FH = 35 – 18

12. 6. Find the side lengths of JKL. Example 3: Using Triangle Classification (see page 217) Step 1 Find the value of x. Step 2 Substitute x into the expressions to find the side lengths. JK = KL 4x – 10.7 = 2x + 6.3 + 10.7 4x = 2x + 17 – 2x –2x 2x = 17 2 x = 8.5 JK = 23.3 JK = 4x – 10.7 JK = 4(8.5) – 10.7 JK = 34 – 10.7 KL = 23.3 KL = 2x + 6.3 KL = 2(8.5) + 6.3 KL = 17 + 6.3 JL = 44.5 JL = 5x + 2 JL = 5(8.5) + 2 JL = 42.5 + 2