1. Lesson 4-2: Congruent Triangles 1 Lesson 4-2 Congruent Triangles

2. Lesson 4-2: Congruent Triangles 2 Congruent Figures Congruent figures are two figures that have the same size and shape. IF two figures are congruent THEN they have the same size and shape. IF two figures have the same size and shape THEN they are congruent. Two figures have the same size and shape IFF they are congruent.

3. Lesson 4-2: Congruent Triangles 3 Congruent Triangles - CPCTC CPCTC: Corresponding Parts of Congruent Triangles are Congruent Two triangles are congruent IFF their corresponding parts (angles and sides) are congruent. B C A Q R P A ↔ P; B ↔ Q; C ↔ R Vertices of the 2 triangles correspond in the same order as the triangles are named. Corresponding sides and angles of the two congruent triangles: ≡ ≡ = = │ │

4. Lesson 4-2: Congruent Triangles 4 Congruent Triangles B A C X Y Z ≡ ≡ = = │ │ ∆ABC  ______  A  ____  Z  B  _____  C  ______  Y  X ∆ ZYX ∆ABC  ∆XYZ Note:

5. Lesson 4-2: Congruent Triangles 5 When referring to congruent triangles (or polygons), we must name corresponding vertices in the same order. R A Y S U N SUNSUN RAYRAY  SUN   RAY Also  NUS   YAR Also  USN   ARY Example…………

6. Lesson 4-2: Congruent Triangles 6 Example ……… M O N T A S R U P E 1.Pentagon MONTA  Pentagon PERSU 2.Pentagon ATNOM  Pentagon USREP 3.Etc. If these polygons are congruent, how do you name them ?

7. Lesson 4-1: Using Properties 7 Lesson 4-1 Using Properties

8. Lesson 4-1: Using Properties 8 Commutative & Associative Property...order does not matter. Addition: a + b = b + a Multiplication: a b = b a 4 + 5 = 5 + 4 2 3 = 3 2 Examples The commutative and associative property does not work for subtraction or division. Commutative Property Associative Property...grouping does not matter Addition: (a + b) + c = a + (b + c) Multiplication: (ab) c = a (bc) (1 + 2) + 3 = 1 + (2 + 3) (23)4 = 2(34)

9. Lesson 4-1: Using Properties 9 Properties for Addition & Multiplication a + = a “0”is the identity element for addition 0 Additive Inverse: a + = 0 a and (-a) are called opposites (-a) Multiplicative Identity “1”is the identity element for multiplication a = a 1 Multiplicative Inversea and are called reciprocals a = 1 Additive Identity:

10. Lesson 4-1: Using Properties 10 Multiplicative & Distributive Property Multiplicative Property of Zero a 0 = ___ 0 Multiplicative Property of -1 a -1 = ___-a The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = a b + aca(b - c) = ab - ac (b + c) a = b a + ca (b - c) a = ba - ca and

11. Lesson 4-1: Using Properties 11 1)5a + (6 + 2a) = 5a + (2a + 6) 2)5a + (2a + 6) = (5a + 2a) + 6 3)2(3 + a) = 6 + 2a Commutative (switch order) Associative (switch groups) Distributive Name the property : Examples………….

12. Lesson 4-1: Using Properties 12 Properties of Equality Addition Subtraction Multiplication Division If a = b, then a + c = b + c a - c = b - c a c = b c a / c = b / c x  0 Substitution:If a = b, then a can be replaced by b Example: (5 + 2)x = 7x

13. Lesson 4-1: Using Properties 13 Properties of Equality & Congruence Reflexive: a = a5 = 5 Symmetric: If a = b then b = a If 4 = 2 + 2 then 2 + 2 = 4 Transitive: If a=b and b=c, then a=c If 4 = 2 + 2 and 2 + 2 = 3 + 1, then 4 = 3 + 1 Reflexive: a  a  A   B Symmetric: If a  b then b  a Transitive: If a  b and b  c, then a  c If  X  Y and  Y  Z, then  X  Z If  C   D, then  D   C