Geometry: Algebraic-Geometric Proofs (2



A #4: Triangle Congruence (SSS-SAS-ASA-HL-AAS) (4.3) Name ____________________________ Pd ___

On a separate sheet of paper, complete each problem. Write a two-column proof proving that the two given triangles are congruent where applicable.

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| |[pic] [pic] |

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|Given: [pic] bisects [pic]; [pic] |Given: [pic], [pic] |

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|Prove: [pic] |Prove: [pic] |

| | Given: [pic], [pic], [pic] |

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| |Prove: [pic] |

| |Given: [pic], [pic] |

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| |Prove: [pic] |

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|Given: [pic], [pic] is the |Given: [pic] bisects [pic], |

|perpendicular bisector of [pic], |[pic], [pic] |

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|Prove: [pic] |Prove: [pic] |

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|Kate and Jaclyn wished to find the distance from N on one side of a lake to P on the other side. So they put| |

|stakes at N, P, and T. Then they extended [pic] to S making sure [pic]. They followed a similar process in | |

|extending [pic] to R. They then measured [pic] and found it to be 70 meters. They concluded that NP was 70 | |

|meters. Prove that they were correct. | |

|Draw your own diagram for this: [pic], [pic], [pic], [pic], [pic], [pic] |

|Solve for x and y. |

|What additional information would you need to prove the triangles congruent by the stated postulate or theorem? |

|SSS |AAS |HL |ASA |SAS |

|[pic] |[pic] |[pic] |[pic] |[pic] |

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|HL |

|[pic] [pic] [pic] [pic] [pic] [pic][pic] |

|SAS | |

|[pic] [pic] | |

|[pic] | |

[pic][pic]

|SSS |ASA |

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|SAS |SSS |

|[pic] |[pic] [pic] |

|AAS Given: [pic] bisects [pic]; [pic] |SAS Given: [pic], [pic] |

|Prove: [pic] |Prove: [pic] |

|SSS |HL Given: [pic], [pic], [pic] |

|[pic] [pic] | |

| |Prove: [pic] |

|ASA |SASGiven: [pic], [pic] |

|[pic] [pic] | |

| |Prove: [pic] |

|HL |SAS |

|[pic] [pic] |[pic][pic] |

|Kate and Jaclyn wished to find the distance from N on one side of a lake to P on the other side. So they put|Draw your own diagram for this. |

|stakes at N, P, and T. Then they extended [pic] to S making sure [pic]. They followed a similar process in |[pic] |

|extending [pic] to R. They then measured [pic] and found it to be 70 meters. They concluded that NP was 70 | |

|meters. Prove that they were correct. | |

|HLGiven: [pic], [pic] is the |AAS Given: [pic] bisects [pic], |

|perpendicular bisector of [pic], |[pic], [pic] |

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|Prove: [pic] |Prove: [pic] |

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|[pic] | |

|SAS | |

|[pic] [pic] |[pic] |

[pic]

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