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.

Solution

Solution Steps

Step 1: Analyze the given information

We are given two triangles $\triangle LGT$ and $\triangle NMQ$. We are also given that $LT \cong NQ$ and $\angle T \cong \angle Q$. 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, $ \triangle LGT $ and $ \triangle MNQ $, with two pairs of corresponding sides marked as congruent: $ LG \cong MN $ and $ 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 $ \angle GLT $ and $ \angle NMQ $.

Final Answer

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

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