Converse of Theorem 2

Q.

In the given figure, ABCD is a quadrilateral. A line through 'D', parallel to AC, meets BC produced in P. Then:

1. Area $\left(\Delta ABP\right)$ = Area $\left(quadABCD\right)$
2. Area $\left(\Delta ABC\right)$ = Area $\left(\Delta ACP\right)$
3. None of the above
4. Area $\left(\Delta BCD\right)$ = Area $\left(quadACPD\right)$

Q. ABCD is a quadrilateral and it becomes a parallelogram if _____.

1. AB$\perp$ CD
2. AB $\parallel$ CD
3. AB = CD
4. AB $\ne$ CD

Q. ______ is not a parallelogram.

1. Square
2. Rectangle
3. Trapezium
4. Rhombus

Q.

In the given figure, ABCD is a quadrilateral. A line through 'D', parallel to AC, meets BC produced in P. Then:

1. Area $\left(\Delta ABP\right)$ = Area $\left(quadABCD\right)$
2. Area $\left(\Delta ABC\right)$ = Area $\left(\Delta ACP\right)$
3. Area $\left(\Delta BCD\right)$ = Area $\left(quadACPD\right)$
4. None of the above

Q. The perpendicular bisector and the angle bisector of an equilateral triangle are the same and they pass through the circumcentre.

1. True
2. False

Q.

The line drawn through the centre of a circle to bisect a chord is __ to the chord.

Q.

If $AB$ is a chord of a circle with center $O,$ and $AC=BC$, then $x={90}^{\circ }$.

1. 80°

2. 90°

Q.

In the figure, $O$ is the centre of the circle of radius $5\text{cm}.$ $P$ and $Q$ are points on chords $AB$ and $CD$ respectively such that $OP\perp AB,OQ\perp CD,AB||CD,AB=6\text{cm}$ and $CD=8cm.$ Determine $PQ$.

1. 8 cm

2. 5 cm

3. 6 cm

4. 7 cm

Q.

$O$ is the centre of the circle of radius $5cm,OP$ is perpendicular to $AB,OQ$ is perpendicular to $CD,AB||CD,AB=6cm$ and $CD=8cm.$ Determine $PQ.$

1. 3cm

2. 4cm

3. 1cm

4. 2cm

Q.

If each of two chords, $AB$ and $CD$, of a circle are at a distance of 4 cm from the centre, then $AB=CD$.

1. True

2. False