Similarly, quadrilateral DPBO is a parallelogram, because
DO || PB and DO PB
(i) In quadrilateral PSOR,
SP | OR (SP is a part of DP and OR is a part of
SQ || PR
So, PSQR is a parallelogram.
Similarly,
EXERCISE 7.1
1. The angles of quadrilateral are in the ratio 3:5:9:13. Find all the angles
quadrilateral
2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
3. Show that if the diagonals of a quadrilateral bisect each other at right angles
is a rhombus.
4. Show that the diagonals of a square are equal and bisect each other at right
6. Show that if the diagonals of a quadrilateral are equal and bisect each othe
angles, then it is a square.
Ac of parallelogram ABCD bisects
Answers
The solution is:
.
There are six important properties of parallelograms to know:
Opposite sides are congruent (AB = DC).
Opposite angels are congruent (D = B).
Consecutive angles are supplementary (A + D = 180°).
If one angle is right, then all angles are right.
The diagonals of a parallelogram bisect each other.
Each diagonal of a parallelogram separates it into two congruent triangles.Parallelogram1
△ACD≅△ABC
If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi.
If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid. The parallel sides are called bases while the nonparallel sides are called legs. If the legs are congruent we have what is called an isosceles trapezoid.
trapetzoid
In an isosceles trapezoid the diagonals are always congruent. The median of a trapezoid is parallel to the bases and is one-half of the sum of measures of the bases.
Trapezoid Median
EF=12(AD+BC.