Triangle Sum Properties

1. Standard:MG 2.3 Draw triangles from given information about them. Triangle Sum Properties Student Objective: -- Students will draw triangles and solve triangle sum problems from given information about them by using equations and scoring an 80% proficiency on an exit slip. Classify triangles and find measures of their angles.

2. A triangleis a polygon with three sides. A triangle with vertices A, B, and C is called “triangle ABC” or “∆ABC.” A B C

3. Classifying Triangles by Sides • A scalene triangle is a triangle with no congruent sides. • An isosceles triangle is a triangle with at least two congruent sides. • An equilateral triangle is a triangle with three congruent sides.

4. Classifying Triangles by Angles • An acute triangle is a triangle with three acute angles. • A right triangle is a triangle with one right angle. • An obtuse triangle is a triangle with one obtuse angle. • An equiangular triangle is a triangle with three congruent angles.

5. Classification By Sides Classification By Angles

6. 1 3 2 Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180o. m<1 + m<2 + m<3 = 180°

7. Property of triangles The sum of all the angles equals 180º degrees. 60º 90º 30º + 60º 180º 30º 90º

8. Property of triangles The sum of all the angles equals 180º degrees. 40º 90º 40º 50º + 180º 50º 90º

9. Property of triangles The sum of all the angles equals 180º degrees. 60º 60º 60º 60º + 180º 60º 60º

10. Ex: 1What is the missing angle? 70º 70º x + x 180º 70º 70º 180– 140 = 40˚

11. EX: 2 What is the missing angle? 90º x 30º x + 180º 90º 30º 180 – 120 = 60˚

12. Ex: 3What is the missing angle? x 60º 60º x + 60º 60º 180º 180 – 120 = 60˚

13. EX 4:What is the missing angle? X 30º 78º X + 78º 30º 180º 180 – 108 = 72˚

14. What is the missing angle? ? 40º 40º ? + 40º 40º 180º 180 – 80 = 100˚

15. Find all the angle measures 35x 45x 10x 180 = 35x + 45x + 10x 180 = 90x 2 = x 90°, 70°, 20°

16. DAY 2: Triangle Sum Theorem Continued Standard : MG 2.2 Use the properties of complementary and supplementary angles and the sum of angles of a triangle to solve problems involving an unknown angle. Student Objective (s): -- Students will use properties of the sum of triangles and solve problems with an unknown angle from given information about them by using equations and scoring an 80% proficiency on an exit slip.

17. What can we find out? The ladder is leaning on the ground at a 65º angle. At what angle is the top of the ladder touching the building? 180 = 65 + 90 + x 180 = 155 + x 25˚ = x

18. Extention to Triangle Sum Theorem The acute angles of a right triangle are complementary. m∠A + m∠B = 90o

19. Find the missing angles. The tiled staircase shown below forms a right triangle. The measure of one acute angle in the triangle is twice the measure of the other angle. Find the measure of each acute angle. Con’t

20. Find the missing angles. SOLUTION: 2x + x = 90 3x = 90 x = 30˚ 2x = 60˚

21. Find the missing angles. 2x + (x – 6) = 90˚ 2x = 2(32) = 64˚ 3x – 6 = 90 3x = 96 (x – 6) = 32 – 6 = 26˚ x = 32

22. Class work Read Lesson 4.1 “Triangle Sum” in your textbook and review the Power Point lesson again.

23. Homework In your textbook: Lesson 4.1/ 1-9, 17, 25