1. Warm Up Check homework answers with each other!

2. Answers 4.1 c worksheet

3. Ch. 4.2: Congruence and Triangles Students will prove triangles congruent using SSS, SAS, ASA, AAS, and HL theorems.

4. Congruence When two figures are congruent they have exactly the same size and the same shape. CongruentNot Congruent

5. There has to be a correspondence between their angles and sides, such that corresponding angles and corresponding sides are congruent. Corresponding Sides Corresponding Angles A B C D EF

6. Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If  A   D and  B   E, then  C   F. A B C D E F

7. Warm Up, Day 2: 1.Write a paragraph or two-column proof to explain why each angle of an equiangular triangle measures 60 0. Determine if each statement below is true or false. Explain your reasoning. 2.If three angles in one triangle are congruent to three angles in another triangle, then the two triangles are congruent. 3.If two sides in one triangle are congruent to two sides in another triangle, then the two triangles are congruent.

8. Properties of Congruent Triangles Reflexive Property of Congruent Triangles Every triangle is congruent to itself. Symmetric Property of Congruent Triangles If  ABC   DEF, then  DEF   ABC. Transitive Property of Congruent Triangles If  ABC   DEF and  DEF   JKL, then  ABC   JKL.

9. Triangle Exploration #1 1.Using the straws provided, cut three different lengths. 2.On a piece of paper, form a triangle with the straws and mark the vertices of the triangle. 3. Remove the straws and draw the sides of your triangle. 4. Have a group member repeat the same process using the same straws. Try to make a triangle that is not congruent to the one you drew.

10. Triangle Exploration #2 1.On a piece of paper, place two straws so their endpoints are at the center of a protractor. Arrange them to form a 45 0 angle. 2.Mark two vertices of a triangle and mark the center of the protractor as the third vertex. 3.Remove the straws and protractor and draw the sides of your triangle. 4.Have your partner repeat the process. Try to make a triangle that has a 45 0 angle, but is not congruent to the one you drew.

11. Ch. 4.3: Proving Triangles are Congruent

12. Warm Up 1.Find the value of the variable. The diagram is not to scale. 2.Find the measure of each interior and exterior angle. The diagram is not to scale.

13. Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

14. Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

15. Given: Prove: A R G D

16. Given: G is the midpoint of Prove: F H E G

17. Given: bisects Prove: A E G C

18. Challenge!!! Given: Prove: HG L J K