Questions: Complete the proof. Given: FG parallel to KL, FG congruent to KL Prove: triangle FGK congruent to triangle KLF Complete the proof below. Statement Reasons 1. FG parallel to KL 1. Given 2. FG congruent to KL 2. Given 3. FK congruent to FK 3.

Complete the proof. Given: FG parallel to KL, FG congruent to KL Prove: triangle FGK congruent to triangle KLF Complete the proof below. Statement Reasons 1. FG parallel to KL 1. Given 2. FG congruent to KL 2. Given 3. FK congruent to FK 3.
Transcript text: Complete the proof. Given: $\overline{\mathrm{FG}} \| \overline{\mathrm{KL}}, \overline{\mathrm{FG}} \cong \overline{\mathrm{KL}}$ Prove: $\triangle F G K \cong \triangle K L F$ Complete the proof below. Statement Reasons 1. $\overline{\mathrm{FG}} \| \overline{\mathrm{KL}}$ 1. Given 2. $\overline{\mathrm{FG}} \cong \overline{\mathrm{KL}}$ 2. Given 3. $\overline{\mathrm{FK}} \cong \overline{\mathrm{FK}}$ 3.
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Solution

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Solution Steps

Step 1: Given Information
  • Statement: \( FG \parallel KL \)
  • Reason: Given
Step 2: Given Information
  • Statement: \( FG \cong KL \)
  • Reason: Given
Step 3: Reflexive Property
  • Statement: \( FK \cong FK \)
  • Reason: Reflexive Property
Step 4: Prove Triangles are Congruent
  • Statement: \( \triangle FGK \cong \triangle KLF \)
  • Reason: SAS (Side-Angle-Side) Congruence Postulate

Final Answer

  • Prove: \( \triangle FGK \cong \triangle KLF \)
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