4-1

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

2. 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. 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. B is an obtuse angle. So BDC is an obtuse triangle. Class Example: Classifying Triangles by Angle Measures Classify BDC by its angle measures. B is an obtuse angle.

12. Therefore mABD + mCBD = 180°. By substitution, mABD + 100°= 180°. SomABD = 80°. ABD is an acute triangle by definition. Class Example: Classifying Triangles by Angle Measures Classify ABD by its angle measures. ABD andCBD form a linear pair, so they are supplementary.

13. Example 1 - 3 Classify EHG, EFH, FHG by its angle measure Triangle EHG is right Triangle EFH is obtuse Triangle FHG is equiangular

14. By Side Lengths Equilateral Triangle Three congruent sides

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

16. By Side Lengths Scalene Triangle No congruent sides

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

18. From the figure, . So HF = 10, and EHF is isosceles. Class Example: Classifying Triangles by Side Lengths Classify EHF by its side lengths.

19. By the Segment Addition Postulate, EG = EF + FG = 10 + 4 = 14. Since no sides are congruent, EHG is scalene. Class Example: Classifying Triangles by Side Lengths Classify EHGby its side lengths.

20. Example # 1 - 3 Classify ABC, ABD and ACD by its side lengths. ABC = equilateral Triangle ABD = Scalene Triangle ACD = scalene

21. Example # 1: Using Triangle Classification Find the side lengths of JKL. Step 1 Find the value of x. JK = KL 4x – 1.3 = x + 3.2 3x = 4.5 x = 1.5

22. Example #1 Continued Find the side lengths of JKL. Step 2 Substitute 1.5 into the expressions to find the side lengths. JK = 4x – 1.3 = 4(1.5) – 1.3 = 4.7 KL = x + 3.2 = 1(1.5) + 3.2 = 4.7 JL = 5x + 0.2 = 5(1.5) +0.2 = 7.3

23. Example # 2 Find the side lengths of equilateral FGH. Step 1 Find the value of y. Given. FG = GH = FH Def. of  segs. Substitute (3y – 4) for FG and (2y + 3) for GH. 3y – 4 = 2y + 3 Add 4 and subtract 2y from both sides. y = 7

24. Check It Out! Example #2 Continued Find the side lengths of equilateral FGH. Step 2 Substitute 7 into the expressions to find the side lengths. FG = 3y – 4 = 3(7) – 4 = 17 GH = 2y + 3 = 2(7) + 3 = 17 FH = 5y – 18 = 5(7) – 18 = 17

25. Homework: Page 219: # 1-19

26. Exit Question Classify each triangle by its angles and sides. 1. MNQ 2.NQP 3. MNP 4. Find the side lengths of the triangle. acute; equilateral obtuse; scalene acute; scalene 29; 29; 23

27. Exit Question Name: Classify each triangle by its angles and sides. 1. MNQ 2.NQP 3. MNP 4. Find the side lengths of the triangle.

28. Exit Question Name: Classify each triangle by its angles and sides. 1. MNQ 2.NQP 3. MNP 4. Find the side lengths of the triangle.