Amaury C.

asked • 03/24/21

Geometry demostration

1-If a triangle has two congruent sides and is not right, prove that the line joining the feet of the heights on the congruent sides is parallel to the third of the sides.


2- Show that the points of the bisector of an angle are equidistant from its sides.


3-Using similarity or congruence, show that if a right triangle has an angle of 30º, then the leg opposite it measures half the hypotenuse.

Mark M.

What are the "feet of the heights"?
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03/24/21

Amaury C.

I don't know :( that why I'm here
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03/24/21

Doug C.

To make this obvious try drawing an obtuse isosceles triangle with one of the congruent sides lying horizontally. Then sketch altitudes from each of the vertices of the acute angles. The foot of each of those altitudes is where it intersects the opposite side. Join those feet with a line segment. Somehow you need to prove that segment is parallel to the 3rd side (long side) of the triangle.
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03/25/21

Doug C.

This will work for any isosceles triangle that is not a right triangle.
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03/25/21

Mark M.

I keep getting a diagonal equal to the third side. How about you?
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03/25/21

1 Expert Answer

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Doug C. answered • 12/16/25

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