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3. Given: RS LTS, RV LTV, and ST = VT Prove: RS RV R COMMON CORE GEOMETRY, UNIT #3-EUCLIDEAN TRIANGLE PROOF AND CONSTRUCTIONS-LESSON #9 S​

3 Given RS LTS RV LTV and ST VT Prove RS RV R COMMON CORE GEOMETRY UNIT 3 EUCLIDEAN TRIANGLE PROOF AND CONSTRUCTIONS LESSON 9

Answer :

Final answer:

In this problem in Common Core Geometry, we are asked to prove a statement about triangle congruence using the given information. This can be done by applying the SAS or HL congruence criteria.

Explanation:

The given problem is from the field of Euclidean Triangle Proof and Constructions in Common Core Geometry. In this problem, we are given that RS LTS, RV LTV, and ST = VT. The objective is to prove that RS RV R. To prove this, we can use triangle congruence theorems such as the Side-Angle-Side (SAS) congruence criterion or the Hypotenuse-Leg (HL) congruence criterion.

Learn more about Triangle Congruence here:

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Rewritten by : Barada

The given statements can be written as follows:

RS = LTS RV = LTV ST = VT

To prove that RS and RV are common, we must prove that the measures of RS and RV are equal. This can be shown by showing that the measures of the corresponding sides of the triangles are equal.

Since ST = VT, the measures of the corresponding sides of the triangles RS and RV are equal. Since these sides have the same measure, it follows that the measures of RS and RV are equal. Therefore, RS and RV are common.