consider the triangles shown. if m∠utv

Question

consider the triangles shown. if m∠utv < m∠uts < m∠str, which statement is true? o vu < us < sr by the hinge theorem. o vu = us = sr by the hinge theorem. o m∠utv = m∠ust = m∠str by the converse of the hinge theorem. o m∠utv > m∠uts > m∠str by the converse of the hinge theorem.

Accepted Answer

# Explanation:
## Step1: Recall hinge - theorem
In two triangles, if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third - side of the first triangle is longer than the third - side of the second triangle.
## Step2: Analyze given angles
We are given that $m\angle UTV<m\angle UTS < m\angle STR$. In $\triangle UTV$, $\triangle UTS$, and $\triangle STR$, assume $UT = UT$ (common side) and $ST=ST$ (common side).
By the hinge theorem, in $\triangle UTV$ and $\triangle UTS$ with $UT$ common and $TV = TS$ (from the figure's equal - length markings), since $m\angle UTV<m\angle UTS$, we have $VU<US$. Also, in $\triangle UTS$ and $\triangle STR$ with $ST$ common and $UT = SR$ (from the figure's equal - length markings), since $m\angle UTS < m\angle STR$, we have $US<SR$. So, $VU<US<SR$.

# Answer:
VU < US < SR by the hinge theorem.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall hinge - theorem

Step2: Analyze given angles

Answer: