Is this enough information to prove that the quadrilateral is a parallelogram?
One pair of opposite sides are congruent Not enough you can find two opposite congruent sides in an isosceles trapezium Diagonals are perpendicular Not enough You can find this situation in a Rhomboid or Kite which is not a parallelogram as well as in a Rhombus which is a parallelogram Two pairs of opposite angles are congruent Enough Equal angles oppose equal sides All pairs of consecutive angles are congruent Only squares but not all parallelograms have all pairs of consecutive angles congruent The information given altogether applies to squares which are parallelograms
Are these enough information to prove that the quadrilateral is a parallelogram?(geometry)?
-one angle is a right angle -two pairs of opposite sides are congruent -consecutive angles are congruent -diagonals are perpendicular and congruent -opposite sides are parallel and congruent -all four sides are congruent for the second one I thought yes for the fifth one i thought yes and for the 6th one i got no are those correct?
Decide if you are given enough information to prove that the quadrilateral is a parallelogram:?
No, not enough information. Squares, rectangles and rhombuses have two pairs of opposite congruent angles as well as parallelograms.
Decide if you are given enough information to prove that the quadrilateral is a parallelogram:?
Not enough information... Proof by counter-example: the diagonals of a rhombus are perpendicular...a rhombus is a parallelogram. the diagonals of a kite are perpendicular...a kite is NOT a parallelogram qed
I have the four sides of an irregular quadrilateral and none of its angles. How can I calculate its area?
Brahmagupta (c.598 - 665) was an Indian mathematician who gave his formula for finding the area of a quadrilateral, which does not require the angle measurements. Only the 4 lengths are sufficient to find the area. We should give him due credit!Brahmagupta's FormulaBrahmagupta's formula finds the area of a cyclic quadrilateral. The formula for the area of a cyclic quadrilateral with sides a, b, c, d is given bywhere s = [a+b+c+d]/2and a, b, c and d are the four sides.Example 1: Let ABCD be a kite. DA = AB = 3, DC = CB = 5. Let us find the area of the kite.s = (3+3+4+4)/2 = 14/2 = 7Area = [(7–3)(7–4)(7–4)(7–3)]^0.5 = (4x3x4x3)^0.5 = 12.As you can see DAC is a RAT as also ABC, with AC as the hypotenuse (5). Therefore area of DAC and ABC = 3*4/2 = 6 each, and so area of ABCD = area DAC + area ABC = 6+6 = 12, same as what we got from Brahmagupta’s formula.Example 2: Let PQRS be a kite. SP = PQ = 5, QR = RS = 12. Let us find the area of the kite.s = (5+5+12+12)/2 = 34/2 = 17Area = [(17–5)(17–12)(17–12)(17–5)]^0.5 = (12x5x5x12)^0.5 = 60.As you can see SPR is a RAT as also PQR, with PR as the hypotenuse (13). Therefore area of SPR and PQR = 5*12/2 = 30 each, and so area of PQRS =area SPR + area PQR = 30 + 30 = 2*30 = 60, same as what we got from Brahmagupta’s formula.
Please decide weather or not you are given enough information to prove the quadrilateral is a parallelogram?
A parallelogram is a special quadrilateral: Its opposite sides are parallel... and you knew that! However, the fact that the opposite sides are parallel results in two things: the opposite sides will be equal in their lengths and the opposite angles will be congruent. This works backward, too: If you have a quadrilateral and it is given that both pairs of opposite angles consist of congruent angles ... it's a parallelogram. If it is given that a quadrilateral has congruent opposite sides ... it's a parallelogram. Another condition which would guarantee that a quadrilateral would be a parallelogram would be to be given that three consecutive angles were right angles. That would mean that the fourth angle was also a right angle and the quadrilateral is a rectangle. Finally, if three consecutive sides of a quadrilateral are congruent it must be a parallelogram... a rhombus or a square.
Determine whether the quadrilateral is a parallelogram. Explain XN = NZ and NY = NW?
A. Yes; if two opposite sides are congruent, then the quadrilateral is a parallelogram. B. No; if the diagonals of a quadrilateral bisect each other, this is not enough to prove that the quadrilateral is a parallelogram. C. No; if two opposite sides are congruent, this is not enough to prove that the quadrilateral is a parallelogram. D. Yes; if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
How can I prove a quadrilateral is a rectangle?
You would need to prove one of the followingOpposite sides are parallel and it has at least 1 90 degree angle (A right paralleogram)It has 3 90 degree angles - then the fourth one must also be 90 degrees and it would then be a rectangleDiagonals of a parallelogram are congruentIt’s a cyclic quadrilateral (It can be inscribed in a circle) and has at least 2 right angles that aren’t opposite anotherOpposite sides (1 pair is enough) are equal length and it has at least 1 right angle