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Geometry, Unit 5 – Congruent Triangles Proof Activity – Part I Name _________________________ For each problem, do the following: a. Show the given information in the diagram (using tick marks to show congruent sides and arcs to show congruent angles) b. Show any other congruent parts you notice (from vertical angles, sides shared in common, or alternate interior angles with parallel lines) c. Give the postulate or theorem that proves the triangles congruent (SSS, SAS, ASA, AAS, HL) d. Finally, fill in the blanks to complete the proof. B
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1. Given: BC ≅ DC ; AC ≅ EC Prove: ΔBCA ≅ ΔDCE C
Statements Reasons 1. 1. Given 2. 2. Vertical ∠s Theorem 3. ΔBCA ≅ ΔDCE 3. 2. Statements 3. A
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Given: JK ≅ LK ; JM ≅ LM Prove: ΔKJM ≅ ΔKLM K
Reasons 1. 1. 2. 2. Reflexive Prop. 3. 3. M
J
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Given: ∠G ≅ ∠I ; FH bisects ∠GFI Prove: ΔGFH ≅ ΔIFH Statements Reasons 1. ∠G ≅ ∠I ; FH bisects ∠GFI 1. 2. ∠GFH ≅ ∠IFH 2. Def. of ___________________ 3. 3. Reflexive Prop. 4. 4. L
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4. 5. 6. Given: ∠N and ∠Q are right angles; NO ≅ PQ Prove: ΔONP ≅ ΔPQO Statements Reasons 1. ∠N and ∠Q are right angles 1. 2. ΔONP and ΔPQO are _________________ triangles 2. Def. of right triangle 3. 3. Reflexive Prop. 4. NO ≅ PQ 4. 5. 5. P
O
Q
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Given: ST || RU ; SR || TU Prove: ΔSRT ≅ ΔUTR Statements Reasons 1. ST || RU 1. 2. 2. If lines ||, alt. int. ∠s ≅ 3. SR || TU 3. 4. ∠SRT ≅ ∠UTR 4. 5. 5. 6. 6. R
U
Given: ∠W and ∠Y are right angles; VX ≅ ZX ; X is the midpoint of WY Prove: ΔVWX ≅ ΔZYX Z
V
Statements Reasons 1. ∠W and ∠Y are right angles 1. 2. 2. Def. of right triangle 3. VX ≅ ZX ; X is the midpoint of WY 3. N
4. 4. Def. of midpoint 5. 5. W
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Y