5 6 Proving Triangles Congruent using ASA and

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5. 6 Proving Triangles Congruent using ASA and AAS Geometry EQ: What other ways

5. 6 Proving Triangles Congruent using ASA and AAS Geometry EQ: What other ways can you prove triangles congruent?

Goals Use ASA and AAS postulates to prove two triangles are congruent. n Solve

Goals Use ASA and AAS postulates to prove two triangles are congruent. n Solve problems using congruence postulates. n 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 2

Included Sides C AC is included between A and C. AB is included between

Included Sides C AC is included between A and C. AB is included between A and B. A 24 November 2020 B CB is included between C and B. Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 3

Theorem 5. 10: Angle-Side-Angle If two angles and the included side of one triangle

Theorem 5. 10: 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 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 4

Example Prove ADB CBD C D Proof: A ADB CBD (Given) S DB (Ref.

Example Prove ADB CBD C D Proof: A ADB CBD (Given) S DB (Ref. ) A B A ABD CDB (Given) ADB CBD (ASA) 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 5

Theorem 5. 11 Angle-Side n If two angles and a nonincluded side of one

Theorem 5. 11 Angle-Side n If two angles and a nonincluded side of one triangle are congruent to corresponding parts of another triangle, then the triangles are congruent. E B A C F D ABC DEF 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 6

Example Is ABC ADC? A Yes, by AAS S A B D A 24

Example Is ABC ADC? A Yes, by AAS S A B D A 24 November 2020 C Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 7

Are these triangles congruent? Yes. Reason: AAS OR AAS. 24 November 2020 Geometry 5.

Are these triangles congruent? Yes. Reason: AAS OR AAS. 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 8

Are these triangles congruent? You could even use ASA. 24 November 2020 Geometry 5.

Are these triangles congruent? You could even use ASA. 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 9

Overlapping Triangles B A 24 November 2020 C D Geometry 5. 6 Proving Triangles

Overlapping Triangles B A 24 November 2020 C D Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 10

Problem: Is ABD DCA? C B 85° A 15° D YES by AAS 24

Problem: Is ABD DCA? C B 85° A 15° D YES by AAS 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 11

Problem: Is ABD DCA? C B 85° A 15° C B 85° D A

Problem: Is ABD DCA? C B 85° A 15° C B 85° D A 15° D YES by AAS 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 12

Methods to show triangles congruent: n. SSS n. SAS n. ASA n. AAS 24

Methods to show triangles congruent: n. SSS n. SAS n. ASA n. AAS 24 November 2020 When trying to determine if triangles are congruent, carefully study the given information, mark the triangles if necessary, then determine what pattern you have. Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 13

T Problem S B A A C A A S S R A What

T Problem S B A A C A A S S R A What other congruence must be given to show that ABC RST using the AAS postulate? BC ST 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 14

T Problem Alternate Solution S A B A C A A S R A

T Problem Alternate Solution S A B A C A A S R A S What other congruence must be given to show that ABC RST using the AAS postulate? BA SR 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 15

T Problem A B S A C S R A S A A What

T Problem A B S A C S R A S A A What other congruence must be given to show that ABC RST using the ASA postulate? AC RT 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 16

State third congruence that must be given to prove the given triangles congruent using

State third congruence that must be given to prove the given triangles congruent using the indicated postulate or theorem. 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 17

1. ASA Theorem. B A F C D E C F 24 November 2020

1. ASA Theorem. B A F C D E C F 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 18

2. AAS Theorem. A C 24 November 2020 B E C F Geometry 5.

2. AAS Theorem. A C 24 November 2020 B E C F Geometry 5. 6 Proving Triangles Congruent: ASA, AAS D F 19

3. SSS B D C F A E CB FE 24 November 2020 Geometry

3. SSS B D C F A E CB FE 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 20

4. SAS Theorem. A B F E C D A D 24 November 2020

4. SAS Theorem. A B F E C D A D 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 21

Is it possible to prove that the triangles are congruent? If so, state the

Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain reasoning 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 22

5. W Yes AAS X 24 November 2020 Z Geometry 5. 6 Proving Triangles

5. W Yes AAS X 24 November 2020 Z Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 23

6. C A Yes SAS D 24 November 2020 R Geometry 5. 6 Proving

6. C A Yes SAS D 24 November 2020 R Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 24

7. The only other thing we know for sure: T S SOT LOF (Vertical

7. The only other thing we know for sure: T S SOT LOF (Vertical Angles) O But this spells… SSA F 24 November 2020 L NOT CONGRUENT Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 25

L S Given: LA || SN, LR NR R Prove: LAR NSR A N

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 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 26

List four ways to show triangles are congruent. SSS n ASA n SAS n

List four ways to show triangles are congruent. SSS n ASA n SAS n AAS n List one way that won’t work. SSA 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 27

Important! To show two triangles congruent, at least one side must be known. n

Important! To show two triangles congruent, at least one side must be known. n Three angles (AAA) does not show congruence (but it is still useful). n 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 28

Summarize 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 29

Summarize 24 November 2020 Geometry 5. 6 Proving Triangles Congruent: ASA, AAS 29