1. Chapter 4 Congruent Triangles

2. 4.1 & 4.6 Triangles and Angles Triangle: a figure formed by three segments joining three noncollinear points. Classification by SIDES Classification by ANGLES EquilateralAcute IsoscelesEquiangular ScaleneRight Obtuse

3. Classification by Sides Equilateral Triangle –3 congruent sides Isosceles Triangle –2 congruent sides Scalene Triangle –No congruent sides

4. Classification by Angles Acute –All angles are acute Equiangular –All angles are congruent Right –One right angle and 2 acute angles Obtuse –One obtuse angle and 2 acute angles

5. Isosceles Triangle Equilateral Triangle Scalene Triangle Classify the following triangles

6. 65° 58°57° 130° Acute scalene Right isosceles Obtuse isosceles

7. Parts of a Triangle A vertex is one of the three points joining sides of a triangle. Two sides sharing a common vertex are adjacent sides.

8. Parts of a right triangle Legs: the sides that form the right angle of the triangle Hypotenuse: the side opposite the right angle

9. Leg Hypotenuse

10. Parts of an isosceles triangle Legs: the two congruent sides Base: the third side

11. Leg Base

12. Angle Measures of Triangles Interior Angles: The three original angles Exterior Angles: The angles adjacent to the interior angles Interior Angles Exterior Angles

13. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°.

14. B A C

15. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. x°x° 2x° X = 30° x + 2x = 90° m  A + m  B = 90  A B

16. More Practice Find the measures of the missing angles: 1 42° 3 2 95° 40° 1 56° 45°1 2 3 50° m  1 = 48° m  1 = 50° m  2 = 40° m  3 = 45° m  1 = 79° m  2 = 51° m  3 = 39°

17. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Remote interior angles Exterior Angle

18. x + 65 = 2x + 10 65° x°x°(2x + 10)° Exterior Angle m  1 = m  A + m  B A B 1 x = 55

19. IsoscelesTriangles Base Angles: The two angles in an isosceles triangle adjacent to the base Vertex Angle: The angle opposite the base Base Angle Vertex Angle

20. Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. A CB

21. Converse to the Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent.

22. Corollary to the Base Angles Theorem If a triangle is equilateral, then it is equiangular.

23. Corollary to the Converse of the Base Angles Theorem If a triangle is equiangular, then it is equilateral.

24. Practice Problems Find the measure of the missing angles. 50° A B C m B=80° m C=50° A B C m A=60° m B=60° m C=60°