Class 9

Math

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Quadrilaterals

If angles A, B, C and D of the quadrilateral ABCD, taken in order are in the ratio 3 : 7 : 6 : 4, then ABCD is a

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In the figure, $ABCD$ is a parallelogram. If $P$ and $Q$ are points on $AD$ and $BC$ respecetively such that $AP=31 AD$ and $CQ=31 BC$, prove that $AQCP$ is a parallelogram.

Find the area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm.

The difference between the semiperimeter and the sides of a $Δ$ABC are 8cm, 7cm and 5cm respectively.Find the area of the triangle.

In the figure, $ABCD$ is a parallelogram in which $∠BAO=35_{o},∠DAO=40_{o}$ and $∠COD=105_{o}$. Calculate $∠CBD$

If the diagonals of a parallelogram are equal and intersect at right angles, then the parallelogram is a square.

The diagonals of a quadrilateral $ABCD$ are perpendicular to each other. Prove that the quadrilateral formed by joining the midpoints of its sides is a rectangle.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . Show that(i) $ΔAPB=∼ΔCQD$(ii) $AP=CQ$

If the area of an equilateral triangle is $813 cm_{2}$, find its height.