SOLUTION: This is a Proving question for Analytical Geometry. Prove analytically that the vertex and the midpoints of the three sides of an isosceles triangle are the vertices of a rhomb

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Question 1078122: This is a Proving question for Analytical Geometry.
Prove analytically that the vertex and the midpoints of the three sides of an isosceles triangle are the vertices of a rhombus.
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Answer by rapture(86) About Me  (Show Source):
You can put this solution on YOUR website!
Try setting the diagram up so that the base is on the x-axis with the left vertex (0,0). Call the right vertex (4a, 0).

Then make the top vertex (which is the vertex of the triangle as well) (2a, 2b).

Then the midpoints are: bottom (2a, 0), left side (a, b) and right side (3a, b).

Draw in the quadrilateral.

Lastly, show that all 4 sides are of the same length by using distance formula.