Advertisements
Advertisements
Question
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35° then find ∠ACB.
Advertisements
Solution
AC = 8 cm ...(i) ...[Given]
`square`ABCD is a rectangle ...[Given]
∴ BD = AC ...[Diagonals of a rectangle are congruent]
∴ BD = 8 cm ...[From (i)]
BO = `1/2` BD ...[Diagonals of a rectangle bisect each other]
∴ BO = `1/2` × 8
∴ BO = 4 cm
side AD || side BC and seg AC is their transversal. ...[Opposite sides of a rectangle are parallel]
∴ ∠ACB = ∠CAD ...[Alternate angles]
∠ACB = 35° ...[∵ ∠CAD = 35°]
∴ BO = 4 cm, ∠ACB = 35°
APPEARS IN
RELATED QUESTIONS
Name the quadrilaterals whose diagonals are equal
ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you)
Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)°. Find the angles of the parallelogram.
In the following figure, ABCD and AEFG are parallelograms. If ∠C = 55°, what is the measure of ∠F?
In the following figure, BDEF and DCEF are each a parallelogram. Is it true that BD = DC? Why or why not?
In Fig. 17.29, suppose it is known that DE = DF. Then, is ΔABC isosceles? Why or why not?
In a rectangle ABCD, prove that ∆ACB ≅ ∆CAD.
A mason has made a concrete slab. He needs it to be rectangular. In what different ways can he make sure that it is rectangular?
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.
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
For which of the following figures, diagonals are equal?
All squares are rectangles.
Every parallelogram is a rectangle.
Every trapezium is a rectangle.
In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA.
A playground is in the form of a rectangle ATEF. Two players are standing at the points F and B where EF = EB. Find the values of x and y.
Construct a rectangle whose one side is 3 cm and a diagonal equal to 5 cm.
