Kevin claims he can draw a trapezoid with three right angles. Is this possible? Explain.

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UhYeaItinkYaKnow UhYeaItinkYaKnow

04-05-2015
Mathematics

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Kevin claims he can draw a trapezoid with three right angles. Is this possible? Explain.

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RedRicin RedRicin · Answer 1 · 2015-05-04T21:34:39-04:00

Using an indirect proof:

Assume that the figure is a trapezoid.
All trapezoids are quadrilaterals.
All quadrilaterals' interior angles add up to 360° because any n-gon's interior angles add up to 180(n-2)°.
We are given that the trapezoid has three right angles.
All right angles are 90°, thus these right angles have a total measure of 270°.
We can conclude fourth angle must be 90°.
If it has four right angles, it is a rectangle.
Rectangles have two sets of parallel sides.
However, trapezoids have exactly one set of parallel sides.
Alas, our figure cannot be a trapezoid.

cclemeno cclemeno · Answer 2 · 2015-05-04T21:42:29-04:00

cclemeno cclemeno

04-05-2015

not possible trapezoid is a quadrilateral with 4 angles and 4 sides which means the interior measure =360 if 3 angles are right the 4th angle must be a right angle a trapezoid does not have 4 right angles,it only has one pair of parallel sides hope this helps

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