Chapter 4 Triangle Congruence

1. Chapter 4 Triangle Congruence By: Emily Gorges, Janie Eyerman, Andie Jamison, and Maria Ong

2. 4-1 Congruence and Transformations Vocab: • dilation-changes size, not shape of a coordinate figure • reflection- a figure reflected over a line • translation-the same figure moved to another place on coordinate grid • rotation- a figure rotated around a vertex to a certain degree

3. 4-2 Classifying Triangles Terms: • Right • Obtuse • Acute • Scalene • Equilateral • Isosceles • Equiangular

4. Example • Classify each triangle- rightobtuse acute scalene equilateral isosceles

5. 4-3 Angle Relationships in Triangles • auxiliary line-a line that is added to a figure to aid in a proof

6. Exterior Angle Theorem • The measure of the exterior angle of a triangle is equal to the sum of its remote interior angles.

7. Third Angle Theorem If two angles of a triangle are congruent to angles of another triangle then the third angles of both triangles are congruent.

8. 4-4 Congruent Triangles Terms: • corresponding angles • corresponding sides • congruent polygons • overlapping triangles

9. Proof example Given: <ACD=<BDC, AC=BD Prove: ACD= BDC <ACD=<BDC G AC=BD G CD=CD Reflexive ACD= BDC SAS* *See slide 11 for SAS

10. 4-5 Triangle Congruence: SSS and SAS Terms • included angle-the angle in between the 2 given sides • side side side-if all 3 sides of a triangle are congruent to the other triangle, then both triangles are congruent • side angle side- the twosides and the included angle are congruent to the other triangle, then both triangles are congruent

11. 4-6 Triangle Congruence: ASA, AAS, and HL • included side- side between the 2 given angles • angle side angle- when the two angles and included side are congruent to the other triangle, then both triangles are congruent • angle angle side- when two angles and a not included side are congruent to the other triangle, then both triangles are congruent • hypotenuse leg- in right triangles when the hypotenuse and one leg are congruent to the other triangle, then both triangles are congruent

12. 4-7 Triangle Congruence: CPCTC Given: CED is isosceles, AE=BE Prove: AC=BD CED is isos. G AE=BE G AEC=BED verticle CE=ED Def. of isos AEC= BED SAS AC=BD CPCTC E

13. 4-9 Isosceles and Equilateral Triangles Isosceles Triangles- a triangle with two sides congruent and the two corresponding angles are congruent A Try It Yourself! Given: AD bisects ABC, Prove: ABC is isosceles B C D

14. Equilateral Triangle- a triangle with all sides and angles are congruent See, all sides and angles ARE congruent!