Parallelograms

Q. A quadrilateral with two pairs of opposite sides parallel is a _____.

1. triangle
2. parallelogram
3. parallel lines
4. trapezium

Q.

The perimeter of the parallelogram is $140cm$. If one of the sides is greater than the other by $10cm,$ find the lengths of the sides of the parallelogram.

Q. In the following figure $\angle$ABD = $\angle$BDC and $\angle$CBD = $\angle$ADB. Then, ABCD is a __________.

1. triangle
2. parallelogram
3. pentagon
4. hexagon

Q. If ABCD is a parallelogram with AB || CD, AD || BC, and BD is the diagonal, then the $△ABD$ and $△BCD$ are always .

1. equilateral
2. isoceles
3. scalene
4. congruent

Q.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD.

Show that $\left(\mathrm{i}\right)\mathrm{\Delta APB}\cong \mathrm{\Delta CQD}$

$\left(\mathrm{ii}\right)\mathrm{AP}=\mathrm{CQ}$

Q. In the figure, which pair of angles represent the adjacent angles?

1. ∠6 and ∠8
2. ∠1 and ∠4
3. ∠5 and ∠7
4. ∠1 and ∠3

Q. Which of the following statement is/are true in case of a parallelogram?

1. Opposite sides are equal
2. Diagonals bisect one another
3. Diagonals are perpendicular to each other
4. Opposite sides are parallel

Q. ABCD is a parallelogram, and BC is twice the length of AB. If the perimeter of ABCD is 360 cm, find the length of AD.

1. 60 cm
2. 80 cm
3. 100 cm
4. 120 cm

Q. If in two triangles ABC and PQR , AB = PQ, AC = PR and BC = QR, then .

1. ∆ ACB ≅ ∆ PQR
2. ∆ ABC ≅ ∆ PQR
3. ∆ ABC ≅ ∆ PRQ

Q.

In the figure, there is a jogging track that has to be renovated. The cost of renovation is Rs. 15 per square meters. For the circular parts, the inner and outer radii are 6 m and 8 m respectively. If the total cost of renovation is Rs. 2, 520, find the length of AB.

1. 10 m

2. 15 m

3. 20 m

4. 25 m

Q.

If the sides of $△ABC$ are AB = 5 cm, BC = 4 cm and CA = 3 cm, and sides of $△PQR$ are PQ = 4 cm, QR = 3 cm and RP = 5 cm, then _______.

1. $△ABC\cong △QPR$
2. $△ABC\cong △PQR$
3. $△ABC\cong △RPQ$
4. $△ABC\cong △PRQ$

Q. The figure, □ABCD is a parallelogram and its diagonals AC and BD intersect at E.
If l(AB) = 3 cm, l (BC) = 5 cm, m∠BAD = 120° and m∠ADC = 60°, then


(1) l (DC) = ?
(2) l (AD) = ?
(3) m∠BCD = ?
(4) m∠ABC = ?

Q. Which of the following statements are true?

1. $△$ABD $\cong$ $△$BCD
2. $△$BMC $\cong$ $△$CMD
3. $△$AMB $\cong$ $△$CMD
4. $△$AMB $\cong$ $△$BMC

Q.

Consider the following figure:

Lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{XY}$ intersect in point O.

Find the value of (y – x).

1. 40°

2. 140°

3. Data insufficient

4. 100°

Q. From the following figure, $\angle$3 and $\angle$4 form _______.

1. alternate interior angles
2. alternate exterior angles
3. vertically opposite angles
4. co-interior angles

Q. How many triangles are there in a rectangle with one diagonal?

1. 1
2. 2
3. 3
4. 4

Q. Construct a triangle $ABC$ whose sides are $4cm,5cm$ and $7cm$. Find the $\angle ACB$

1. $co{s}^{-1}\frac{-1}{5}$
2. $co{s}^{-1}\frac{2}{5}$
3. $co{s}^{-1}\frac{3}{5}$
4. $co{s}^{-1}\frac{4}{5}$

Q. If in two triangles ABC and PQR , AB = PQ, AC = PR and BC = QR, then .

1. ∆ ACB ≅ ∆ PQR
2. ∆ ABC ≅ ∆ PRQ
3. ∆ ABC ≅ ∆ PQR

Q. In the figure, which pair of angles represent the adjacent angles?

1. ∠1 and ∠3
2. ∠5 and ∠7
3. ∠1 and ∠4
4. ∠6 and ∠8

Q. The adjacent angles of a parallelogram are _____.

1. complementary
2. supplementary
3. equal
4. none of the above

Q. If $△ART\cong △PEN,$ using the SSS criterion, then $RT=?$