Advertisements
Advertisements
Question
Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.
Advertisements
Solution
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
RELATED QUESTIONS
Name the quadrilaterals whose diagonals are equal
The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.
The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.
In Fig. 17.29, suppose it is known that DE = DF. Then, is ΔABC isosceles? Why or why not?
Diagonals of a parallelogram ABCD intersect at O. AL and CM are drawn perpendiculars to BD such that L and M lie on BD. Is AL = CM? Why or why not?
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 and 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 in the following, so as to make the statement true:
A square is a rhombus in which .....
In a rectangle ABCD, prove that ∆ACB ≅ ∆CAD.
State with Reason Whether the Following Statement is ‘True’ Or ‘False’.
Every rectangle is a parallelogram.
If diagonal of a rectangle is 26 cm and one side is 24 cm, find the other side.
ABCD is a rectangle, if ∠BPC = 124°
Calculate:
- ∠BAP
- ∠ADP
The following figure is a rectangle in which x: y = 3: 7; find the values of x and y.
A quadrilateral whose opposite sides and all the angles are equal is a ______.
If diagonals of a quadrilateral are equal, it must be a rectangle.
Every parallelogram is a rectangle.
In rectangle READ, find ∠EAR, ∠RAD and ∠ROD
A rectangular MORE is shown below:
Answer the following questions by giving appropriate reason.
- Is RE = OM?
- Is ∠MYO = ∠RXE?
- Is ∠MOY = ∠REX?
- Is ΔMYO ≅ ΔRXE?
- Is MY = RX?
