Advertisements
Advertisements
प्रश्न
Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.
Advertisements
उत्तर
Given: `square`ABCD is a rectangle.
To prove: `square`ABCD is a parallelogram.
Proof:
`square`ABCD is a rectangle.
∠A = ∠B = ∠C = ∠D = 90° ...(angles of rectangle)
∠A = ∠B = ∠C = ∠D ...(each angle 90°)
A quadrilateral is a parallelogram if its pairs of opposite angles are congruent.
∴ `square`ABCD is a parallelogram.
APPEARS IN
संबंधित प्रश्न
Explain why a rectangle is a convex quadrilateral.
In a parallelogram ABCD, the diagonals bisect each other at O. If ∠ABC = 30°, ∠BDC = 10° and ∠CAB = 70°. Find:
∠DAB, ∠ADC, ∠BCD, ∠AOD, ∠DOC, ∠BOC, ∠AOB, ∠ACD, ∠CAB, ∠ADB, ∠ACB, ∠DBC and ∠DBA.
In the following figure, BDEF and DCEF are each a parallelogram. Is it true that BD = DC? Why or why not?
Which of the following statement is true for a rectangle?
Its diagonals are equal.
Which of the following statement is true for a rectangle?
Its diagonals are perpendicular and bisect each other.
Which of the following statement is true for a rectangle?
All rectangles are squares.
Which of the following statement are true for a square?
It has all its sides of equal length.
Fill in the blank of the following, so as to make the statement true:
A square is a rectangle in which .....
In a rectangle ABCD, prove that ∆ACB ≅ ∆CAD.
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
Draw a rectangle whose one side measures 8 cm and the length of each of whose diagonals is 10 cm.
Draw a square whose each side measures 4.8 cm.
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35° then find ∠ACB.
State with Reason Whether the Following Statement is ‘True’ Or ‘False’.
Every rectangle is a parallelogram.
Adjacent sides of a rectangle are 7 cm and 24 cm. Find the length of its diagonal.
Diagonals of a rectangle PQRS are intersecting in point M. If ∠QMR = 50° find the measure of ∠MPS.
For which of the following figures, all angles are equal?
For which of the following figures, diagonals are equal?
Every trapezium is a rectangle.
Every rectangle is a trapezium.
