4-5 Triangle Congruence: ASA, AAS & HL Geometry

4-5 Triangle Congruence: ASA, AAS & HL Post 4-5-1 Angle-Side-Angle (ASA)  post If 2 s and the included side of one Δ are  to the corresponding s and included side of another Δ, then the 2 Δs are .

B (( C ) If A  Z, C  X and , then Δ ABC  Δ ZYX. A Y ( Z )) X

Thm 4-5-2 Angle-Angle-Side (AAS)  thm If 2 s and a non-included side of one Δ are  to the corresponding s and non-included side of another Δ, then the 2 Δs are .

If A  R, C  S, and , then ΔABC  ΔRQS. ) A If A  R, C  S, and , then ΔABC  ΔRQS. (( C S )) Q ) R

Thm 4-5-3 Hypotenuse-Leg (HL) Congruence If the hypotenuse and a leg of a rt are to the hypotenuse and a leg of another rt then the ‘ s are .

Ex. 1) Is it possible to prove the Δs are ? ( ) )) )) (( ) ( (( _______________ ____________

Example 2 Given that B  C, D  F, M is the midpoint of seg DF Prove Δ BDM  Δ CFM B C ) ) (( )) D M F

Proof for Ex. 2 Statements Reasons ________________ ___________________ 2. _________________ 3. ________________ Reasons 1. ________________ 2._________________ 3. ________________

Example 3 X ) (( W Z (( ) Y Given that bisects XZY and XWY Prove that Δ WZX @ Δ WZY X ) (( W Z (( ) Y

Proof for Ex. 3 Statements 1.________________ __________________ 2. _______________ 3. _________________ 4. _________________ Reasons 1. _________________ 2. _________________ 3. ________________ 4. _________________

Example 4) Determine if you can use the HL Congruence Theorem to prove the triangles are congruent. ABE and DCE, given that E is the midpoint of A B E C D no

THERE IS NO AAA (CAR INSURANCE) OR BAD WORDS

Assignment

4.5 Using  Δs Geometry

Once you know that Δs are , you can state that their corresponding parts are . CPCTC-corresponding parts of @ triangles are @.

CPCTC Ex 1: P N L ) ( M

Proof 1: Statements 1. 2. ΔPMN  ΔPML Reasons Given Reflex. Prop Def’n angle bisector SAS CPCTC

Assignment

Proof 1. Given A  R,C  S, 2. 3rd angles thm 3. ASA post 2. B  Q 3. Δ ABC  Δ RQS