Questions: A conjecture and the flowchart proof used to prove the conjecture are shown. Given: S is the midpoint of R. U S ≅ R S Prove: △S T U is an isosceles triangle. Drag an expression or phrase to each box to complete the proof.

A conjecture and the flowchart proof used to prove the conjecture are shown.

Given: S is the midpoint of R.

U S ≅ R S

Prove: △S T U is an isosceles triangle.

Drag an expression or phrase to each box to complete the proof.

Transcript text: A conjecture and the flowchart proof used to prove the conjecture are shown. Given: $S$ is the midpoint of $R$. \[ \overline{U S} \cong \overline{R S} \] Prove: $\triangle S T U$ is an isosceles triangle. Drag an expression or phrase to each box to complete the proof. $\square$ $\square$ US $\triangle S T U$ is an isosceles triangle.

Solution

Solution Steps

Step 1: Given Information

The problem states that $ S $ is the midpoint of $ RT $ and $ US = RS $. We need to prove that $ \triangle STU $ is an isosceles triangle.

Step 2: Definition of Midpoint

Since $ S $ is the midpoint of $ RT $, by definition, $ RS = ST $.

Step 3: Given

We are given that $ US = RS $.

Step 4: Prove $ \triangle STU $ is Isosceles

From the given information and the definition of midpoint, we have $ US = ST $. Therefore, $ \triangle STU $ has two equal sides, making it an isosceles triangle.

Final Answer

\[ \triangle STU \text{ is an isosceles triangle.} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!