Advertisements
Advertisements
Question
ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?
Advertisements
Solution

AC = BD (Given)
& AC ⊥ BD (Given)
i.e. Diagonals of a quadrilateral are equal and they are ⊥ to each other.
∴ ABCD is square.
APPEARS IN
RELATED QUESTIONS
Given a parallelogram ABCD. Complete each statement along with the definition or property used.

- AD = ______
- ∠DCB = ______
- OC = ______
- m∠DAB + m∠CDA = ______
Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.
In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.
ABCD is a parallelogram. What kind of quadrilateral is it if: AC = BD but AC is not perpendicular to BD?
In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.

Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = ______.

Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.
Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and ∠B = 60°.
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
