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Question
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35° then find ∠ACB.
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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°
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