Questions: Below are two triangles. segment BC= segment KL angle C= angle L angle B= angle K Based on the information given about the triangles, what method could be used to prove the two triangles are congruent? a. SAS b. ASA c. The triangles cannot be proven congruent. d. SSS

Below are two triangles. segment BC= segment KL angle C= angle L angle B= angle K Based on the information given about the triangles, what method could be used to prove the two triangles are congruent? a. SAS b. ASA c. The triangles cannot be proven congruent. d. SSS
Transcript text: Below are two triangles. segment $B C=$ segment $K L$ angle $C=$ angle $L$ angle $B=$ angle $K$ Based on the information given about the triangles, what method could be used to prove the two triangles are congruent? a. SAS b. ASA c. The triangles cannot be proven congruent. d. SSS
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Solution

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Solution Steps

Step 1: Identify Given Information

The problem provides the following information about two triangles:

  • Segment BC is congruent to segment KL.
  • Angle C is congruent to angle L.
  • Angle B is congruent to angle K.
Step 2: Determine Congruence Criteria

To determine which method can be used to prove the triangles are congruent, we need to consider the given information and match it with the triangle congruence criteria:

  • SAS (Side-Angle-Side)
  • ASA (Angle-Side-Angle)
  • SSS (Side-Side-Side)
Step 3: Apply the ASA Congruence Criterion

The given information includes two angles and the side between them:

  • Angle C = Angle L
  • Segment BC = Segment KL
  • Angle B = Angle K

This matches the ASA (Angle-Side-Angle) criterion for triangle congruence.

Final Answer

The method that can be used to prove the two triangles are congruent is: b. ASA

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