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What is the sum of either pair of opposite angles of a cyclic quadrilateral?
Wiki User
∙ 12y ago
consider cyclicquadrilateral ABCD. Then sum of A + C equalls 180 degree. Also B + D equalls 180
Wiki User
∙ 12y ago
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Describe the methods to prove that a quadrilateral is a rectangle?
you can prove any one of these statements to prove that quadrilateral is a rectangle: -- Opposite sides are parallel and any one angle is a right angle. -- Opposite sides are equal and any one angle is a right angle. -- All four angles are right angles. -- Adjacent angles are complementary, and one of them is a right angle. -- Opposite sides are either equal or parallel, and area is equal to the product of two adjacent sides. -- Diagonals are equal.
Which 2-D shapes can have 2 acute angles and 2 obtuse angles?
With 2 acute and 2 obtuse angles it has 4 angles - the shape is a quadrilateral. The shape can be one of trapezium, parallelogram, rhombus, kite or a general quadrilateral. With the two acute angles next to each other (forcing the two obtuse angles to be next to each other) the shape can be either a trapezium or a general quadrilateral.
Is a rhombus acute?
No. Except for the case of a square (a special case of rhombus), a rhombus will have 2 congruent acute angles, and 2 congruent obtuse angles. The square has 4 right angles. In fact, every quadrilateral will have either all 4 angles equal to right angle (square and rectangle), or will have at least 1 obtuse angle (also at least 1 acute).
How do you prove a quadrilateral is a rectangle?
You need to prove that there are two pairs of sides with equal lengths. Imagine a rectangle A C B D Since side AB is equal in length to side CD that is one equal pair. Likewise, AC is equal to BD and is the other equal pair. Since there are two equal parallel pairs, the angles must all be 90 degrees by rules of geometry so it is a rectangle. Note: The same thing may be used to prove a square, except a square has all sides of the same length. ================================================ If you can prove any one of these statements, then your quadrilateral is a rectangle: -- Opposite sides are parallel and any one angle is a right angle. -- Opposite sides are equal and any one angle is a right angle. -- All four angles are right angles. -- Adjacent angles are complementary, and one of them is a right angle. -- Opposite sides are either equal or parallel, and area is equal to the product of two adjacent sides. -- Diagonals are equal.
Why are opposite angles in a parallelogram equal?
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.
What is the proof to show that sum of either pair of opposite angles in a cyclic quadrilateral is 180 degrees?
Because the 4 interior angles of any quadrilateral add up to 360 degrees and a cyclic quadrilateral diagonals opposite angles add up to 180 degrees therefore it follows that the other pair must be 180 degrees
What is a Quadrilateral with all right angles and a opposite side that is congruent?
This is either a square or a rectangle.
I am a quadrilateral that has 4 right angles. My opposite sides are parallel and of equal length. What figure am I?
A quadrilateral with 4 right angles and opposite sides that are parallel can be either a rectangle if the adjacent sides are of different length or a square if the adjacent sides are of the same length.
What is a quadrilateral with angles congruent?
Either a square or a rectangle.
How do you draw a parallelogram?
i don't no either does it have equal sides? or not? although i no its a quadrilateral and has opposite angles and equal parallel sides
Describe the methods to prove that a quadrilateral is a rectangle?
you can prove any one of these statements to prove that quadrilateral is a rectangle: -- Opposite sides are parallel and any one angle is a right angle. -- Opposite sides are equal and any one angle is a right angle. -- All four angles are right angles. -- Adjacent angles are complementary, and one of them is a right angle. -- Opposite sides are either equal or parallel, and area is equal to the product of two adjacent sides. -- Diagonals are equal.
How do you find a parallelogram in a quadrilateral?
It's not a matter of 'finding' it. Either the quadrilateral is a parallelogram,or else it is not one.If the opposite sides of the quadrilateral are parallel, then it's a parallelogram.
What would be a quadrilateral with 2 right angles?
It could be either a right trapezium, or a kite.
What is quadrilateral with two right angles and pair of parallel sizes?
Either a square or a rectangle.
Can a parallelogram always be inscribed in a circle?
No. For example, if one angle measures 100 degrees, and its adjacent angle is 80 degrees, then the opposite angles would be either 200 or 160 degrees, but in order for a quadrilateral to be inscribed in a circle the opposite angles would have to equal 180 degrees. A parallelogram can be inscribed in a circle if it is a rectangle.
Why cant a quadrilateral have exactly 3 right angles?
A quadrilateral can only have either 2 right angles or four. As you may (or may not) know, the angles in a quadrilateral must add up to 360 degrees. If you have 3 right angles that adds up to 270 degrees, so the last side must also be 90 degrees.
Which 2-D shapes can have 2 acute angles and 2 obtuse angles?
With 2 acute and 2 obtuse angles it has 4 angles - the shape is a quadrilateral. The shape can be one of trapezium, parallelogram, rhombus, kite or a general quadrilateral. With the two acute angles next to each other (forcing the two obtuse angles to be next to each other) the shape can be either a trapezium or a general quadrilateral.
