Special Parallelogram Questions?

Question

Of a parallelogram, rectangle,rhombus,or square, name the two that can have a diagonal conruent to a side. Explain your reasoning

Thanks!!! I really appreciate yalls help!

another question: so of the two quads (rhombus and parallelogram) which one's diaonal length can be determined unambiguously given a side length

Answer 1

Definitely not a rectangle or square. The diagonal in those shapes is part of a right triangle and no matter how hard you try the hypotenuse will never equal a leg. If it did, one of the sides would be zero, and that's not much of a rectangle or square.

For a diagonal to be equivalent to a side, the only shapes that would work are a rhombus and a parallelogram.

If you can imagine drawing two equilateral triangles (all 3 sides the same) and putting them back to back, you would form a rhombus (and also a parallelogram). The diagonal is the same as the four sides.

Answer 2

Only a rhombus and a parallelogram (since a rhombus is a special case of the parallelogram).

The length of the diagonal for a rectangle or square is always the hypotenuse of a triangle with the length and width the two legs. So the hypotenuse will always be larger than either leg.

The angles of a rhombus can be changed. Think about it. If you stick two equilateral triangles together, the two triangles form one rhombus. And the shorted diagonal is equal to the length of the sides of the rhombus.

Answer 3

parallelogram and rhombus.

for the other two (square and rectangle), the diagonal would be part of a right triangle, and for that the hypotenuse can never equal the length of a side.

Answer 4

PQ = RS m+1 = 3k-3 m - 3k = -4 (1) RS = QR 2k = m m - 2k = 0 (2) (1) - (2) -k = -4 so k =4 m = 2k = 2 x 4 = 8 Therefore PQ = 9 , QR = 8 , RS = 9 & SP = 8