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Opposite angles of quadrilaterals in general can vary over quite a range of degrees. In order for a quadrilateral to be a parallelogram, two sets of parallel lines intersect. Imagine a parallelogram resting on its base. Focus on one of the base interior angles. Now flip the parallelogram so that its top is now the base. The shapes will be completely congruent, both in angle size and lengths of sides. Parallelogram is simply a special class of quadrilateral, and this property is part of how parallelograms are defined.
Alternative Answer:
It is rather difficult to prove a geometric proposition while working within the limitations of this browser! But here goes:
Call the parallelogram is ABCD with AB parallel to DC horizontal, and AD parallel to BC.
Consider AD and BC which are parallel, with transversal DC. Then the interior angles on the same side are supplementary. That is, angles ADC and DCB are supplementary.
Now consider AB and DC which are parallel, with transversal AD. Then the interior anlges on the same side are supplementary. That is, angles BAD and ADC are supplementary.
So in the above two paragraphs we have shown that angles ADC + DCB = BAD + ADC
therefore angle DCB = angle BAD [subtracting angle ADC from both sides]
that is, one pair of opposite angles are equal.
You can prove the other pair is equal either by the fact that they are supplementary to these, or by the symmetry of the argument.
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∙ 12y ago
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Quadrilateral with opposite sides and angles equal?
A parallelogram has opposite sides and angles congruent which means of equal measure.
Can a parallelogram be a square?
Yes it can - since the definition of a parallelogram is that it is a quadrilateral with opposite sides (and angles) equal.
What is a parallelogram with all sides congruent but not the angles?
A rhombus has all sides equal but not angles. The opposite angles in a rhombus are equal though.
If a quadrilateral is a parallelogram then its opposite angles are always supplementary?
False because it will have 2 equal opposite obtuse angles and 2 equal opposite acute angles with the 4 angles adding up to 360 degrees.
What quadrangle as equal opposite angles but not right angles and opposite side are parallel and equal in length?
Any parallelogram, including rhombus, but not including rectangle or square.
What is the measurements of opposite angles in a parallelogram?
Opposite angles of a parallelogram are equal.
Are opposite angles of a parallelogram not congruent?
A parallelogram has 2 equal opposite acute angles and 2 equal opposite obtuse angles.
Are the opposite angles of a parallelogram equal?
are the opposite angle of parallelogram equal
How do you match the angles of a parallelogram?
The opposite angles of a parallelogram are equal so math up the opposite angles.
Describe the relationships of the angles in a parallelogram?
The opposite angles in a parallelogram are defined to be equal.
Is there 4 angles in a parallelogram?
Yes, a parallelogram has four sides and four internal angles, the opposite side lengths are equal and the opposite angles are equal.
What is an opposite angle on a parallelogram?
Opposite angles are equal
Are opposite angles in a parrallelogram equal?
Yes, opposite angles in a parallelogram must be equal.
Are opposite angles of a parallelogram equal?
Yes.
What polygon has the opposite angles equal?
parallelogram
Does a parallelogram have equal angles?
Yes, the opposite interior angles of a parellelogram are equal.
Does a parallelogram have 2 equal angles?
Yes, opposite angles are equal in a parallellgram.
