Triangle Congruency Proofs

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New York State Common Core Math Geometry, Module 1, Lesson 26 & Lesson 27

Worksheets for Geometry

Student Outcomes

  • Students complete proofs requiring a synthesis of the skills learned in the last four lessons.

Triangle Congruency Proofs


Exercises for Lesson 26

  1. Given: 𝐴𝐡 βŠ₯ 𝐡𝐢, 𝐡𝐢 βŠ₯ 𝐷𝐢
    𝐷𝐡 bisects ∠𝐴𝐡𝐢, 𝐴𝐢 bisects ∠𝐷𝐢𝐡
    𝐸𝐡 = 𝐸𝐢
    Prove: β–³ 𝐡𝐸𝐴 β‰… β–³ 𝐢𝐸𝐷

  2. Given: 𝐡𝐹 βŠ₯ 𝐴𝐢, 𝐢𝐸 βŠ₯ 𝐴𝐡
    𝐴𝐸 = 𝐴𝐹
    Prove: β–³ 𝐴𝐢𝐸 β‰…β–³ 𝐴𝐡𝐹

  3. Given: 𝑋𝐽 = π‘ŒπΎ, 𝑃𝑋 = π‘ƒπ‘Œ, π‘šβˆ π‘π‘‹π½ = π‘šβˆ π‘π‘ŒπΎ
    Prove: π½π‘Œ = 𝐾𝑋

  4. Given: 𝐽𝐾 = 𝐽𝐿, 𝐽𝐾 βˆ₯ π‘‹π‘Œ
    Prove: π‘‹π‘Œ = 𝑋𝐿

  5. Given: ∠1 β‰… ∠2, ∠3 β‰… ∠4
    Prove: 𝐴𝐢 β‰… 𝐡𝐷

  6. Given: π‘šβˆ 1 = π‘šβˆ 2, π‘šβˆ 3 = π‘šβˆ 4, 𝐴𝐡 = 𝐴𝐢
    Prove: (a) β–³ 𝑨𝑩𝑫 β‰… β–³ 𝑨π‘ͺ𝑫
    (b) π’Žβˆ πŸ“ = π’Žβˆ 6

Exercises for Lesson 27

  1. Given: 𝐴𝐡 = 𝐴𝐢, 𝑅𝐡 = 𝑅𝐢
    Prove: 𝑆𝐡 = 𝑆𝐢

  2. Given: Square 𝐴𝐡𝐢𝑆 β‰… Square 𝐸𝐹𝐺𝑆,
    𝑅𝐴𝐡, 𝑅𝐸𝐹
    Prove: β–³ 𝐴𝑆𝑅 β‰… β–³ 𝐸𝑆𝑅

  3. Given: 𝐽𝐾 = 𝐽𝐿,𝐽𝑋 = π½π‘Œ
    Prove: 𝐾𝑋 = πΏπ‘Œ

  4. Given: 𝐴𝐷 βŠ₯ 𝐷𝑅, 𝐴𝐡 βŠ₯ 𝐡𝑅,
    𝐴𝐷 β‰… 𝐴𝐡
    Prove: βˆ π·πΆπ‘… β‰… βˆ π΅πΆπ‘…

  5. Given: 𝐴𝑅 = 𝐴𝑆, 𝐡𝑅 = 𝐢𝑆,
    𝑅𝑋 βŠ₯ 𝐴𝐡, π‘†π‘Œ βŠ₯ 𝐴𝐢
    Prove: 𝐡𝑋 = πΆπ‘Œ

  6. Given: 𝐴𝑋 = 𝐡𝑋, π‘šβˆ π΄π‘€π΅ = π‘šβˆ π΄π‘Œπ‘ = 90Β°
    Prove: π‘π‘Œ = 𝑁𝑀

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