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Geometry Question: If the median to a side is a triangle is also an altitude to that side, then the triangle is isosceles. (#8 in picture)

Geometry Question: If the median to a side is a triangle is also an altitude to that-example-1
User Bennett Hardwick
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1 Answer

17 votes
17 votes

8.

A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. So:


\begin{gathered} AM\cong MB \\ MC\cong CM_{\text{ }}Reflexive_{\text{ }}property \\ m\angle AMC\cong m\angle BMC_{\text{ }}Perpendicular_{\text{ }}bisector \end{gathered}

Therefore:


\Delta AMC\cong\Delta BMC_{\text{ }}SAS_{\text{ }}Theorem
m\angle CAM\cong\angle CBM_{\text{ }}CPCTC

We can conclude that:


\Delta ABC

Is an isosceles triangle

Geometry Question: If the median to a side is a triangle is also an altitude to that-example-1
User EndlessSpace
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