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Problem 25 Easy Difficulty

Make a conclusion based on the Hinge Theorem or its converse. (Hint: Draw a sketch.)
$\triangle R S T$ is isosceles with base $\overline{R T}$. The endpoints of $\overline{S V}$ are vertex $S$ and a point $V$ on $\overline{R T}$. $R V=4,$ and $T V=5$

Answer

$$\mathrm{m} \angle \mathrm{HSV}<\mathrm{m} \angle \mathrm{PSV}$$

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Video Transcript

we're going to see what information we can conclude from some described triangles. Let's start with triangle RST. And we know that triangle RST is. I saw sleaze with a base or tea. So if this is the base we know that s t and s Are are our congruent legs of our triangle the endpoints of S V R Vertex s and point Viane rt. So that means we've got an interior segment starting at point s landing at point V on segment rt. If RV is four, that's from our TV is four and TV is five from T two v is five. What can we conclude based on this being a congruent segment? SV congruent to itself because of reflexive property. The converse of Hinge there, um, states that we've got two pairs of corresponding convergent sides in two triangles. Segment SV divided our large triangle into two smaller triangles. Therefore, the angle opposite of the longer side is going to be our larger angle. The angle opposite of the smaller side is going to be our smaller angle, so we can conclude that the measurement of angle T s the is a larger angle than the measurement of angle here. Yes, V again, that's using the converse hinge, dirham

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