Focus : How can we prove triangles congruent? Do Now: From what you remember, list some methods of proving triangles congruent. HW: Workbook pg 67 # 2, 8

All three corresponding sides are congruent SSS All three corresponding sides are congruent

SSS – Practice Try solving using the Side-Side-Side method Given : Rectangle ABCD Prove : ▲ABC ▲ACD A D C B

Two angles and an included side are congruent. ASA Two angles and an included side are congruent.

ASA – Practice Try solving using the Angle-Side-Angle method Given : BC bisects Angles ABC and ADC Prove : ▲ABD▲BCD A B D C

Two sides and an included angle are congruent SAS Two sides and an included angle are congruent

SAS- Practice Try solving using the Side-Angle-Side method Given : - Angles ADB and CDB are right angles -ADDC Prove: Triangles ABD and BCD are congruent. B A C D

Two sides and a non-included angle are congruent AAS Two sides and a non-included angle are congruent *Note: I made a mistake on the worksheet – the diagram for AAS is actually supposed to look like this:

AAS- Practice Try solving using the Angle-Angle-Side method Given- AC  BD - ED ║ AF - Angle AFB  Angle CED A B C D E F

Hy-Leg  Hy-Leg Two right triangles are congruent if their hypotenuse and one leg are congruent.

Hy-Leg - Practice Try solving using the Hy-Leg  Hy-Leg method Given: - Right triangles ABD and CDB -Angle BAD  Angle BCD Prove: Triangle ABD  Triangle BCD B C A D

Worksheet Complete the worksheet in groups.

Which method can NOT be used to prove ? Worksheet GIVEN: 1. Which method can NOT be used to prove ? a-SSS b-SAS c-AAS d-HL e-ASA

Worksheet (cont.)

3. Is ABC DBC? If so, name the postulate or theorem used. 2.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.  3.   Is ABC DBC? If so, name the postulate or theorem used.    1.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.  4.  List the methods of proving triangles congruent.   5.  Does HL imply that SSA can be used to prove triangle congruent? Explain your answer.   6. Which of the following is NOT a valid test for congruent triangles?  SSA,  ASA , AAS , or SAS 

10. Is ABC DEC? If so, name the postulate or theorem used. 7.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.    8.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.    9. Given: B is the midpoint of FC. AB and FD bisect each other. AD  BC   Prove: angle ADF  angle F      10. Is ABC DEC? If so, name the postulate or theorem used.    11.   Given: BD is the median of AC. BA  BC   Prove: ABD CBD    12. Given: ABBE, EFBE, BC DE, AD CF   Prove: Angle A  Angle F