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
Name the quadrilaterals whose diagonals are equal
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.
Which of the following statement is true for a rectangle?
It has two pairs of equal sides.
Which of the following statement is true for a rectangle?
Its diagonals are equal.
Which of the following statement true for a square?
Its diagonals are equal to its sides.
Fill in the blank in the following, so as to make the statement true:
A rectangle is a parallelogram in which .....
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
Draw a square whose each side measures 4.8 cm.
State with reason whether the following statement is ‘true’ or ‘false’.
Every parallelogram is a rectangle.
Diagonals of a rectangle PQRS are intersecting in point M. If ∠QMR = 50° find the measure of ∠MPS.
Draw a rectangle ABCD such that l(AB) = 6.0 cm and l (BC) = 4.5 cm.
ABCD is a rectangle, if ∠BPC = 124°
Calculate:
- ∠BAP
- ∠ADP
ABCD is a rectangle whose diagonals AC and BD intersect at O. If ∠OAB = 46°, find ∠OBC
Show that the bisectors of angles of a parallelogram form a rectangle
For which of the following figures, diagonals are equal?
If the adjacent angles of a parallelogram are equal, then the parallelogram is a ______.
All squares are rectangles.
In a rectangle ABCD, AB = 25 cm and BC = 15. In what ratio does the bisector of ∠C divide AB?
In rectangle READ, find ∠EAR, ∠RAD and ∠ROD
