VIEWS: 19 PAGES: 27 POSTED ON: 3/10/2012
Geometry 4.4 Proving Triangles Congruent Worksheet 4.4A mbhaub@mpsaz.org Goals Use ASA and AAS postulates to prove two triangles are congruent. Solve problems using congruence postulates. March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 2 Included Sides AC is included C between A and C. AB is included between A and B. CB is included between C and B. A B March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 3 Postulate 21: Angle-Side-Angle If two angles and the included side of one triangle are congruent to corresponding parts of another triangle, then the triangles are congruent. (ASA) C Z A B X Y ABC XYZ March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 4 Example Prove ADB CBD D C Proof: A ADB CBD (Given) S DB DB (Ref.) A B A ABD CDB (Given) ADB CBD (ASA) March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 5 Theorem 4.5 Angle-Angle-Side If two angles and a nonincluded side of one triangle are congruent to corresponding parts of another triangle, then the triangles are congruent. B E A C F D ABC DEF March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 6 Example Is ABC ADC? A Yes,by AAS S A B D A C March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 7 Are these triangles congruent? Yes. Reason: AAS OR AAS. March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 8 Are these triangles congruent? You could even use ASA. March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 9 Overlapping Triangles B C A D March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 10 Problem: Is ABD DCA? B C 85° 85° 15° 15° A D YES by AAS March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 11 Problem: Is ABD DCA? B C B C 85° 85° 85° 85° 15° 15° 15° 15° A D A D YES by AAS March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 12 Methods to show triangles congruent: SSS When trying to determine if triangles are congruent, SAS carefully study the given information, mark the ASA triangles if necessary, then determine what AAS pattern you have. March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 13 T Problem S S A B A S A C R A A What other congruence must be given to show that ABC RST using the AAS postulate? BC ST March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 14 T Problem Alternate Solution A S B S A C A R A A S What other congruence must be given to show that ABC RST using the AAS postulate? BA SR March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 15 T Problem A B S A C S A R A S A What other congruence must be given to show that ABC RST using the ASA postulate? AC RT March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 16 1. ASA post. B F D A C E C F March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 17 2. AAS Post. A B E D C C F F March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 18 3. SSS B D C F A E CB FE March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 19 4. SAS Post. F E A C D B A D March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 20 5. W Yes AAS X Z March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 21 6. C A Yes SAS D R March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 22 7. The only other thing we T know for sure: S SOT LOF (Vertical Angles) O But this spells… SSA L F NOT CONGRUENT March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 23 L S Given: LA || SN, LR NR R Prove: LAR NSR A N 1. LA || SN 1. Given 2. L N 2. Alt. int s 3. LR NR 3. Given 4. LRA NRS 4. Vert s 5. LAR NSR 5. ASA March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 24 List four ways to show triangles are congruent. SSS ASA SAS AAS List one way that won’t work. SSA March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 25 Important! To show two triangles congruent, at least one side must be known. Three angles (AAA) does not show congruence (but it is still useful). March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 26 Homework Page 223 Problems 8 – 19 all Check the odds when finished Tomorrow: review and practice all of the triangle congruence postulates. March 10, 2012 Geometry 4.4 Proving Triangles Congruent: ASA, AAS 27 7