Math  /  Geometry

QuestionVV is the midpoint of RT\overline{R T} and SU\overline{S U}. Complete the proof that STVURV\triangle S T V \cong \triangle U R V. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & VV is the midpoint of RT\overline{R T} & Given \\ 2 & VV is the midpoint of SU\overline{S U} & Given \\ 3 & RUST\overline{R U} \cong \overline{S T} & Given \\ 4 & RVTV\overline{R V} \cong \overline{T V} & \\ 5 & SVUV\overline{S V} \cong \overline{U V} & \\ 6 & STVURV\triangle S T V \cong \triangle U R V & \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. V V is the midpoint of RT \overline{R T} and SU \overline{S U} .
2. RUST \overline{R U} \cong \overline{S T} is given.
3. We need to prove STVURV \triangle S T V \cong \triangle U R V .

STEP 2

1. Use the definition of a midpoint.
2. Apply the congruence criteria for triangles.

STEP 3

Since V V is the midpoint of RT \overline{R T} , by definition, RVTV \overline{R V} \cong \overline{T V} .

STEP 4

Since V V is the midpoint of SU \overline{S U} , by definition, SVUV \overline{S V} \cong \overline{U V} .

STEP 5

Now, we have three pairs of congruent segments: - RVTV \overline{R V} \cong \overline{T V} (from Step 1) - SVUV \overline{S V} \cong \overline{U V} (from Step 2) - RUST \overline{R U} \cong \overline{S T} (given)

STEP 6

Using the Side-Side-Side (SSS) Congruence Postulate, we can conclude that STVURV \triangle S T V \cong \triangle U R V because all corresponding sides are congruent.
The proof is complete, and we have shown that STVURV \triangle S T V \cong \triangle U R V .

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