3.3 Parallel Lines and the Triangle Angle-Sum Theorem

1. 3.3 Parallel Lines and the Triangle Angle-Sum Theorem Geometry Ms. Keish 9/15/08

2. 2 Standard/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: Classify triangles by their sides and angles. Find angle measures in triangles DEFINITION: A triangle is a figure formed by three segments joining three non-collinear points.

3. 3 Names of triangles

4. 4 Acute Triangle

5. 5 Equiangular triangle 3 congruent angles. An equiangular triangle is also acute.

6. 6 Right Triangle 1 right angle

7. 7 Parts of a triangle Each of the three points joining the sides of a triangle is a vertex.(plural: vertices). A, B and C are vertices. Two sides sharing a common vertext are adjacent sides. The third is the side opposite an angle

8. 8 Right Triangle Red represents the hypotenuse of a right triangle. The sides that form the right angle are the legs.

9. 9 An isosceles triangle can have 3 congruent sides in which case it is equilateral. When an isosceles triangle has only two congruent sides, then these two sides are the legs of the isosceles triangle. The third is the base.

10. 10 Identifying the parts of an isosceles triangle Explain why ?ABC is an isosceles right triangle. In the diagram you are given that ?C is a right angle. By definition, then ?ABC is a right triangle. Because AC = 5 ft and BC = 5 ft; AC ?BC. By definition, ?ABC is also an isosceles triangle.

11. 11 Identifying the parts of an isosceles triangle Identify the legs and the hypotenuse of ?ABC. Which side is the base of the triangle? Sides AC and BC are adjacent to the right angle, so they are the legs. Side AB is opposite the right angle, so it is t he hypotenuse. Because AC ?BC, side AB is also the base.

12. 12 Using Angle Measures of Triangles

13. 13 Ex. 3 Finding an Angle Measure. Triangle Exterior Angle theorem: m?1 = m ?A +m ?1

14. 14 Finding angle measures Corollary to the triangle sum theorem The acute angles of a right triangle are complementary. m ?A + m ?B = 90?

15. 15 Finding angle measures X + 2x = 90 3x = 90 X = 30? So m ?A = 30? and the m ?B=60?