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.

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 smaller than the included angle of the second triangle, then the third - side of the first triangle is shorter than the third - side of the second triangle.
In $\triangle UTV$, $\triangle UTS$, and $\triangle STR$, assume $UT = UT$ (common side) and $TS=TS$ (common side).
We are given that $m\angle UTV<m\angle UTS < m\angle STR$.
## Step2: Apply hinge - theorem
By the hinge theorem, in $\triangle UTV$ and $\triangle UTS$ with $UT$ common and $TV = TS$ (not given explicitly but in the context of the hinge - theorem application), since $m\angle UTV<m\angle UTS$, we have $VU < US$.
In $\triangle UTS$ and $\triangle STR$ with $TS$ common and $UT = SR$ (not given explicitly but in the context of the hinge - theorem application), since $m\angle UTS<m\angle STR$, we have $US < SR$.
So, $VU<US < SR$.

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall hinge - theorem

Step2: Apply hinge - theorem

Answer: