1. 4.1 Triangles and Angles Geometry Mrs. Spitz Fall 2004

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 4.1 Homework 4.1 Worksheet A and B Chapter 4 Definitions – pg. 192 Chapter 4 Postulates/Theorems – green boxes within chapter 4 Binder check Monday/Tuesday

4. 4 Names of triangles Equilateral —3 congruent sides Isosceles Triangle—2 congruent sides Scalene— no congruent sides Triangles can be classified by the sides or by the angle

5. 5 Acute Triangle 3 acute angles

6. 6 Equiangular triangle 3 congruent angles. An equiangular triangle is also acute.

7. 7 Right Triangle 1 right angle Obtuse Triangle

8. 8 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 adjacent Side opposite  A

9. 9 Right Triangle Red represents the hypotenuse of a right triangle. The sides that form the right angle are the legs. hypotenuse leg

10. 10 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. leg base Isosceles Triangles

11. 11 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. About 7 ft. 5 ft

12. 12 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. About 7 ft. 5 ft leg Hypotenuse & Base

13. 13 Using Angle Measures of Triangles Smiley faces are interior angles and hearts represent the exterior angles Each vertex has a pair of congruent exterior angles; however it is common to show only one exterior angle at each vertex.

14. 14 Ex. 3 Finding an Angle Measure. 65  xx Exterior Angle theorem: m  1 = m  A +m  1 (2x+10)  x  + 65  = (2x + 10)  65 = x +10 55 = x

15. 15 Finding angle measures Corollary to the triangle sum theorem The acute angles of a right triangle are complementary. m  A + m  B = 90  2x x

16. 16 Finding angle measures X + 2x = 90 3x = 90 X = 30  So m  A = 30  and the m  B=60  2x x C B A