1. Angles and Triangles Objective: Geometry Rules for Angles and Triangles

2. NameMeasureExample Right Angle Acute Angle Obtuse Angle Straight Angle 90 0 < X < 90 90< X < 180 180

3. Pairs of Angles Name/DefinitionExample Adjacent angles Vertical angles ** Theorem Linear pair **Theorem 2 coplanar  s that have a common vertex, but no common internal points 2 nonadjacent  s formed by 2 intersectIng lines. Vertical  s are  A pair of adjacent  s whose Common sides are opposite Rays (forms a line). The sum of the measures of the  s in a linear pair = 180. A C B D A B E D C ABC D

4. Pairs of Angles (Cont.) Name/DefinitionExample Complementary  s Supplementary  s Perpendicular Lines: 2  s whose sum = 90 2  s whose sum = 180 1 2 AB C D Lines that intersect to form 4 right  s. A E C D B

5. Classifying Triangles by Angles Acute ΔObtuse ΔRight ΔEquiangular Δ All angles are acute One angle is obtuse One angle is 90º All angles are 

6. Classifying Triangles by Sides Scalene ΔIsosceles ΔEquilateral Δ No 2 sides are  At least 2 sides are  All sides are 

7. The Triangle Angle-Sum Theorem The sum of the measure of a triangle is 180. A B C m  A + m  B + m  C = 180

8. Examples Classify each triangle by their sides and angles. 1.2. Find the value of x. 3. 4.5.

9. 6. In isosceles triangle  ABC,  B is the vertex angle. If the m  A = 4x + 7 and m  C = 2x + 21, find the  C. 7. Find x. 8. Find the measure of the sides of equilateral  ABC if AB = 6x – 5 and BC = 2x + 11. (4x + 7)  xx 28 

10. Centroid The centroid divides each median in the ratio 2:1 FE D 9. AG = 24 and GD = 2x – 9 BC = 5y – 2 DC = 3y + 9. Solve for x and y. AG = 2GD BG = 2GE CG = 2FG

11. Triangle Midsegment Theorem A midsegment of a triangle is _______ to one side of the triangle, and its length is If B and D are midpoints of AC and EC then _______ ________ // ½ the length of that side.

12. 10.11.