1. Lesson 1 Menu 1.Refer to the figure. What is the special name given to the pair of angles shown by  2 and  6? 2.Refer to the figure. Find m  3. 3.Refer to the figure. Find m  4. 4.Find the slope of the line that contains the points at (4, 4) and (2, –5). 5.What is the slope of a line that is perpendicular to the line

2. Lesson 1 MI/Vocab acute triangle Identify and classify triangles by angles. Identify and classify triangles by sides. obtuse triangle right triangle equiangular triangle scalene triangle isosceles triangle equilateral triangle

3. Lesson 1 KC1

4. Lesson 1 Ex1 Classify Triangles by Angles A. ARCHITECTURE The triangle truss below is modeled for steel construction. Use a protractor to classify ΔJMN, ΔJKO, and ΔOLN as acute, equiangular, obtuse, or right.

5. Lesson 1 Ex1 Answer: ΔJMN has one angle with measure greater than 90, so it is an obtuse triangle. ΔJKO has one angle with measure equal to 90, so it is a right triangle. ΔOLN is an acute triangle with all angles congruent, so it is an equiangular triangle. Classify Triangles by Angles

6. A.A B.B C.C D.D Lesson 1 CYP1 A.acute B.equiangular C.obtuse D.right A. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔABC.

7. A.A B.B C.C D.D Lesson 1 CYP1 A.acute B.equiangular C.obtuse D.right B. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔACD.

8. A.A B.B C.C D.D Lesson 1 CYP1 A.acute B.equiangular C.obtuse D.right C. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔADE.

9. Lesson 1 KC2

10. Lesson 1 Ex2 Isosceles triangles have at least two sides congruent. Classify Triangles by Sides A. Answer: ΔUTX and ΔUVX are isosceles.

11. Lesson 1 Ex2 B. Scalene triangles have no congruent sides. Classify Triangles by Sides Answer: ΔVYX, ΔZTX, ΔVZU, ΔYTU, ΔVWX, ΔZUX, and ΔYXU are scalene.

12. Lesson 1 CYP2 1.A 2.B 3.C 4.D A.ΔABC and ΔABD B.ΔADE and ΔAEB C.ΔBED and ΔACB D.ΔACD and ΔACB A. Which of the following triangles are isosceles?

13. Lesson 1 CYP2 1.A 2.B 3.C 4.D A.ΔABE B.ΔACE C.ΔADE D.ΔABD B. Which of the following triangles is scalene?

14. Lesson 1 Ex3 Find Missing Values ALGEBRA Find d and the measure of each side of equilateral triangle KLM if KL = d + 2, LM = 12 – d, and KM = 4d – 13. Since ΔKLM is equilateral, each side has the same length. So KL = KM. Substitution Subtract d from each side. Add 13 to each side. Divide each side by 3. 5 = d 2 = 3d – 13

15. Lesson 1 Ex3 Find Missing Values Next, substitute to find the length of each side. Answer: For ΔKLM, d = 5 and the measure of each side is 7.

16. 1.A 2.B 3.C 4.D Lesson 1 CYP3 A.x = 10 and all sides are 3. B.x = 6 and all sides are 13. C.x = 3 and all sides are 10. D.x = 3 and all sides are 16. ALGEBRA Find x and the measure of each side of equilateral triangle ABC if AB = 6x – 8, BC = 7 + x, and AC = 13 – x.

17. Lesson 1 Ex4 Use the Distance Formula COORDINATE GEOMETRY Find the measures of the sides of ΔRTS. Classify the triangle by sides.

18. Lesson 1 Ex4 Use the distance formula to find the lengths of each side. Use the Distance Formula Answer: since all 3 sides have different lengths, ΔRST is scalene.

19. A.A B.B C.C D.D Lesson 1 CYP4 A.scalene B.isosceles C.equilateral D.cannot be determined Find the measures of the sides of ΔABC. Classify the triangle by sides.