Questions: What other information, if any, do you need to prove the two triangles congruent by SAS? Explain. Choose the correct answer below. A. GT ≅ NQ is needed because the congruent angles need to be included between two corresponding congruent sides. B. LT ≅ MQ is needed because the congruent angles need to be included between two corresponding congruent sides. C. LT ≅ MQ and GT ≅ NQ are both needed because all three corresponding sides must be congruent. D. No additional information is needed to prove the triangles congruent by SAS.

What other information, if any, do you need to prove the two triangles congruent by SAS? Explain.

Choose the correct answer below.
A. GT ≅ NQ is needed because the congruent angles need to be included between two corresponding congruent sides.
B. LT ≅ MQ is needed because the congruent angles need to be included between two corresponding congruent sides.
C. LT ≅ MQ and GT ≅ NQ are both needed because all three corresponding sides must be congruent.
D. No additional information is needed to prove the triangles congruent by SAS.
Transcript text: What other information, if any, do you need to prove the two triangles congruent by SAS? Explain. Choose the correct answer below. A. $\overline{\mathrm{GT}} \cong \overline{\mathrm{NQ}}$ is needed because the congruent angles need to be included between two corresponding congruent sides. B. $\overline{L T} \cong \overline{M Q}$ is needed because the congruent angles need to be included between two corresponding congruent sides. C. $\overline{\mathrm{LT}} \cong \overline{\mathrm{MQ}}$ and $\overline{\mathrm{GT}} \cong \overline{\mathrm{NQ}}$ are both needed because all three corresponding sides must be congruent. D. No additional information is needed to prove the triangles congruent by SAS.
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Solution

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Solution Steps

Step 1: Analyze the given information

We are given two triangles LGT\triangle LGT and NMQ\triangle NMQ. We are also given that LTNQLT \cong NQ and TQ\angle T \cong \angle Q. We want to prove the triangles congruent by SAS.

Step 2: Determine the required information for SAS congruence

SAS congruence states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of### Step 1: Identify the Given Information The problem provides two triangles, LGT \triangle LGT and MNQ \triangle MNQ , with two pairs of corresponding sides marked as congruent: LGMN LG \cong MN and LTMQ LT \cong MQ .

Step 2: Understand the SAS Congruence Criterion

The SAS (Side-Angle-Side) criterion for triangle congruence states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Step 3: Determine the Missing Information

To apply the SAS criterion, we need to know that the included angles between the given pairs of congruent sides are also congruent. In this case, the included angles are GLT \angle GLT and NMQ \angle NMQ .

Final Answer

The correct answer is: B. GLTNMQ \angle GLT \cong \angle NMQ is needed because the congruent angles need to be included between two corresponding congruent sides.

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