1.  1. If two triangles are congruent, then they have matching________ and ________. 2. Complete the congruence statement.

2. 1.  T2. m  I3. CA 4. IG5. ΔATC6. ΔBGI 7.  E,  F,  S,  T 8. Definition of  Δs 9.  L   F,  X   N,  R   E, LX  FN, XR  NE, LR  FE 10.a. ΔKROb.  K, CPCTc. KO, CPCT d.  R, CPCT Alt Int  s are  11.a. ΔRLAb. RL c.  3, CPCTLR, Alt Int  s are  d.  4, CPCTPL, AR, Alt Int  s are 

3. Section 4-2 Some Ways to Prove Triangles Congruent

4. When we talk about congruent triangles, we mean everything about them is congruent. All 3 pairs of corresponding angles are equal…. And all 3 pairs of corresponding sides are equal

5. For us to prove that 2 people are identical twins, we don’t need to show that all “2000” body parts are equal. We can take a short cut and show 3 or 4 things are equal such as their face, age and height. If these are the same I think we can agree they are twins. The same is true for triangles. We don’t need to prove all 6 corresponding parts are congruent. We have 5 short cuts or methods. Today we will look at 3 methods.

6. SSS If we can show all 3 pairs of corresponding sides are congruent, then the triangles are congruent.

7. SAS If we can show 2 pairs of sides and the included angles are congruent, then the triangles are congruent. Includedangle Non-includedangles

8. This is called a common side. It is a side for both triangles. We will be using the reflexive property to state the common side.

9. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. X Y Z M L N XYZ = LMN by ASA Post. ~

11. Which method can be used to prove the triangles are congruent?

12. Common side SSS Parallel lines alt int angles Common side SAS Vertical angles SAS

18.  You must use theorems, postulates, and definitions to deduce sides/angles are congruent.  “It looks the same” will not suffice.

19. StatementsReasons 1. E is the midpt. of MJ.1. Given. 2. Def. of midpt. 3. Given 5. TE=TE5. Reflexive Prop. 6. SAS Postulate T J E M

20.  Pg 124-126 Written Exercises  #1-17 All