Q1.
What is the sum of the interior angles of a quadrilateral?
360
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Q2.
In the adjoining figure, diagonals PR and QS intersect at O. If OR = 8 cm and OS = 6 cm, calculate the area of quadrilateral PQRS.
96 sq.cm
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Q3.
Which of the following is the property of every parallelogram?
Q4.
Name the quadrilateral whose diagonals are equal, bisect each other, but are not perpendicular.
Rectangle
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Q5.
Which of the following statement is correct?
Q6.
Name the quadrilateral whose diagonals are equal and perpendicular bisector of each other.
Square
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Q7.
Name the parallelogram whose diagonals bisect each other at right angle but are not equal.
Rhombus
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Q8.
Which of the following statement is not true?
Q9.
Name the quadrilateral in which only one pair of opposite sides is parallel but not equal in length.
Q10.
Which of the following is not a property of rectangle?
Q11.
If one angle of a parallelogram is \(70^\circ\), what will be the measure of its adjacent angle?
110
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Q12.
In a parallelogram ABCD, diagonals meet at O. If AC = 10 cm, then the length of AO is:
Q13.
If three angles of a quadrilateral are \(90^\circ, 80^\circ \text { and } 100^\circ\), what is the measure of fourth angle?
90
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Q14.
In a parallelogram ABCD, if AB = 6 cm, BC = 8 cm, then the perimeter is:
Q15.
If diagonals of a quadrilateral are equal but do not bisect each other, then it is:
Q16.
If a parallelogram has all sides equal but diagonals are not equal, then it is a:
Q17.
In which of the following quadrilateral, the pairs opposite sides are parallel but diagonals are not equal?
Q18.
What is the the relationship between the angle formed by the bisectors of any two adjacent angles of a parallelogram to the sum of the pair of adjacent angles?
Q19.
In a rhombus ABCD, if \(\angle ACB = 40^\circ\), then the measure of \(\angle BCD\) is:
Q20.
In quadrilateral ABCD, diagonals AC and BD bisect each other at right angle. if \(\angle ADB = 40^\circ\), then the measure of \(\angle DCB\) is:
Q21.
In rectangle PQRS, if \(\angle PRS = 50^\circ \), then what will be the measure of \(\angle PSQ\)?
40
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Q22.
In a rectangle ABCD, the diagonal AC is inclined to side AB at \(25^\circ\). What is the measure of angle between the diagonal AC and side AD?
65
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Q23.
What type of quadrilateral is obtained by joining the midpoints of the sides of a quadrilateral?
Parallelogram
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Q24.
The quadrilateral formed by the bisectors of the angles of a parallelogram is a:
Q25.
In a parallelogram ABCD, if \(\angle A = (2x + 25)^\circ\) and \(\angle B = (3x - 5)^\circ\), what is the value of x?
32
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Q26.
PQRS is a rhombus with \(\angle PQR = 120^\circ \). what is the measure of \(\angle QSR\)?
60
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Q27.
The quadrilateral formed by joining the mid-points of the sides of a rectangle is a:
Q28.
What type of quadrilateral is formed by joining the mid points of the sides of a rhombus?
Rectangle
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Q29.
In parallelogram ABCD, if \(\angle A = 2\angle B\), then the measure of \(\angle D\) is:
Q30.
PQRS is a parallelogram in which \(\angle Q = \angle P\). The measure of \(\frac{1}{2}(\angle R + \angle S\)) is:
Q31.
In a quadrilateral ABCD, AB = CD and AD = BC. If \(\angle A = 90^\circ\), then ABCD is a:
Q32.
What is a trapezium with equal non-parallel sides called?
Isosceles trapezium
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Q33.
The perimeter of a parallelogram is 22cm. If the longer side measures 6.5cm what is the length of the shorter side?
4.5 cm
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Q34.
In the given figure, \(∠A = 50^\circ, ∠B = 60^\circ\) and \(∠C = 70^\circ\). What is the measure of \(\angle DFE\)?
60
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Q35.
In the given figure, A, B and C are the mid points of sides QR, RP and PQ respectively. If PQ = PR, then the quadrilateral ABPC is a:
Q36.
M, N and P are mid-points of AB, AC and BC respectively. If MP = 6 cm, then what is the length of side AN?
6 cm
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Q37.
In the given figure, M, N and P are mid-points of AB, AC and BC respectively. If MN = 3 cm, NP = 3.5 cm and MP = 2.5 cm, then the perimeter of \(\triangle ABC\) is:
Q38.
The ratio of the perimeter of the triangle formed by joining the midpoints of the sides of a given triangle to the perimeter of the given triangle is:
Q39.
In quadrilateral ABCD, the bisectors of \(∠A \) and \(∠B \) intersect at O such that \(∠AOB = 75^\circ\). Find the value of \(∠C + ∠D\).
150
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Q40.
If PQRS is a square, then what is the measure of \(∠SRP\)?
45
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Q41.
The diagonals of a rhombus are 12cm and 16cm. Find the length of each side.
10 cm
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Q42.
The diagonals AC and BD of a parallelogram ABCD intersect at O. If OA = 3.5 cm and OD = 2.5 cm. What is the length of AC?
7 cm
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Q43.
In the given figure, PQRS is a parallelogram in which \(\angle PSR = 130^\circ\). The measure of \(\angle RQT\) is:
Q44.
The angles of a quadrilateral are in the ratio 1:2:3:4 . The measure of its greatest angle is:
Q45.
If the length of the diagonal of a square is \(10\sqrt {2}\) cm what is the length of each side?
10 cm
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Q46.
One of the diagonals of a rhombus is 24 cm and its side is 13 cm. What is the length of the other diagonal?
10 cm
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Q47.
The angles of a quadrilateral are in the ratio 3:5:9:13. The measure of the smallest angle of the quadrilateral is:
Q48.
In \(\triangle ABC\), D and E are the midpoints of sides AB and AC respectively. then the relation of DE and BC is:
Q49.
The line segment joining the midpoints of two sides of a triangle is ______ to the third side.
Q50.
In a triangle, if the midpoints of all three sides are joined, the large triangle is divided into how many congruent triangles?
Q51.
The Midpoint Theorem states that in \(∆ABC\), \(DE = \frac{1}{2} BC\). This relation is valid only if D and E are:
Q52.
If D is the midpoint of AB and \(DE \parallel BC\) cuts AC at E, then AE:EC is:
Q53.
The line drawn through the midpoint of one side of a triangle parallel to another side ______ the third side.
Q54.
In an equilateral triangle of side 12cm, what is the length of the segment joining the midpoints of any two sides?
6 cm
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Q55.
Diagonals of a parallelogram ABCD intersect at O. If \(\angle BOC = 90º\) and \(\angle BDC = 50º\), then \(\angle OAB\) is:
Q56.
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:
Q57.
Which of the following is not true for a parallelogram?
Q58.
All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?
Rectangle or square
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Q59.
What is the maximum number of obtuse angle a quadrilateral can have?
3
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Q60.
One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.
84
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Q61.
In the adjoining figure, a quadrilateral PQRS is formed by joining the mid-points the sides of a rhombus. What is the measure of \(\angle QPS\)?
90
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Q62.
What is the number of acute angles a quadrilateral can have at most?
3
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Q63.
Diagonals of a quadrilateral ABCD bisect each other. If \(\angle A = 35º\), determine the measure of \(∠B\).
145
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Q64.
In the adjoining figure, AX and CY are respectively the bisectors of the opposite angles A and C of a parallelogramABCD. Then:
Q65.
X and Y are respectively the mid-points of the opposite sides AD and BC of a parallelogram ABCD. Also, BX and DY intersect AC at P and Q, respectively. Which of the following is incorrect?
Q66.
If a diagonal of a parallelogram bisects one of its interior angles, then the parallelogram is necessarily a:
Q67.
In the adjoining figure, the diagonal PR of a rhombus PQRS is produced to T. If \(\angle SRT = 152^\circ\), then the value of x is:
Q68.
In the given figure, l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p. Which theorem proves that G is a midpoint of AF?
Q69.
In the given figure, l, m, and n are parallel lines cut by transversals t, p, and q. If B is equidistant from A and C, which of the following is false?
Q70.
In the given figure, AD is the median and \(DE \parallel AB\). Which of the following statement is valid?
Q71.
In the given figure, ABCD is a rectangle. P and Q are mid - points of AD and DC respectively. The length of PQ is:
Q72.
Two diagonals are equal in a:
Q73.
Diagonals necessarily bisect opposite angles in a:
Q74.
ABCD and PQRS are rectangle where Q is the mid-point of BD. If QR = 5 cm, then the length of the side AB is:
Q75.
In \(∆PQR\), if QR = 10 cm and \(EF\parallel QR\) where E and F are mid-points of sides PQ and QR respectively. Then the length of EF is equal to:
Q76.
ABCD is a quadrilateral in which P, Q, R and S are the midpoints of the sides AB, BC, CD and DA respectively. AC is a diagonal. Then:
Q77.
In a parallelogram, sum of its two adjacent angles is:
Q78.
ABC is a trapezium in which \(AB || DC\), BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F. Then:
Q79.
In a quadrilateral ABCD, \(\angle D = 150^\circ\) and \(\angle A = \angle B = \angle C\). Find the measures of \(\angle A\).
70
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Q80.
In the given figure, ABCD is a parallelogram. AP and CQ are perpendiculars from vertices A and C on the diagonal BD. Then:
Q81.
In the adjoining figure, ABCD is a parallelogram, \(AE \perp DC\) and \(CF \perp AD\). If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.
12.8 cm
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Q82.
In the given figure, if two points X and Y are taken on diagonal PR such that \(△QXR \cong△RYP\), then the quadrilateral PQRS is necessarily a:
Q83.
PQRS is a rhombus with \(\angle PQR = 120^\circ \). The measure of \(\angle PRS\) is :
Q84.
Find the measure of the angle of a parallelogram which is \(30^\circ\) less than twice its adjacent angle.
110
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Q85.
What is the measure of the angle of a parallelogram which is equal to the measure of its adjacent angle?
90
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Q86.
If the diagonal AC of rectangle ABCD bisects \(\angle A\) as well as \(\angle C\), then ABCD is a ______.
Square
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Q87.
In the given figure, ABCD is a square. Find the value of x.
Rhombus
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Q88.
If P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD and \(AC ⊥ BD\), then PQRS is precisely a ______.
Square
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Q89.
In the adjoining figure, AC = 6 cm and BC = 8 cm. Find the length of CM.
5 cm
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Q90.
The sum of two opposite angles of a quadrilateral is \(220°\). The other two angles of the quadrilateral are equal. Find the measure of each equal angles.
70
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Q91.
In the adjoining figure, QX is the medians of \(∆PQR\). What is the ratio of PX:RX?
1:1
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Q92.
In the adjoining figure, AD and BE are the medians of \(∆ABC\) and \( DF \parallel BE\). What is the ratio of CF:AC?
1:4
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Q93.
In the adjoining figure, ZQ and PQ are the medians of \(∆XYZ\) and \( ∆ZQX\) respectively. If XY = XZ, determine the ratio of XY:XP.
2:1
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Q94.
In a quadrilateral PQRS, opposite angles are equal. If SR = 2 cm and PR = 5 cm, the determine the length PQ.
2 cm
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Q95.
In the adjoining figure, ABCD is a parallelogram. If E and F are the midpoints of sides AB and CD respectively, how many other triangles are congruent to △APE?
3
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Q96.
The line segments joining the mid-points of the opposite sides of a quadrilateral _____ each other.
Bisect
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Q97.
D and E are the midpoints of sides AB and AC respectively of \(△ABC\). DE is produced to F such that \(CF \parallel AD\). Name the quadrilateral DFCB formed.
Parallelogram
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Q98.
In \(∆ABC\), AB = 5 cm, BC = 8 cm and CA = 7 cm. If points D, E and F are respectively the mid-points of AB, BC and AC, determine the perimeter of \(∆DEF\).
10 cm
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Q99.
In the adjoining figure, BDEF and FDCE are parallelograms. Which theorem best proves that 2DE= AB?
Converse of Midpoint Theorem
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Q100.
In the adjoining figure, ABCD and AEFG are two parallelograms. If \(∠C = 55^\circ\), determine the measure of \(∠AGF\).
125
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Q101.
If BC = 12 cm, AB = 14.8 cm, AC = 12.8 cm, determine the perimeter of quadrilateral BCYX.
31.8 cm
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Q102.
The figure, given below, shows a trapezium ABCD. M and N are the mid-points of the non-parallel sides AD and BC respectively. Find the length of side DC, if MN = 15 cm and AB = 23 cm.
7 cm
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Q103.
A parallelogram ABCD has P the mid-point of DC and Q a point of AC such that \(CQ = \frac {1}{4}AC\). PQ produced meets BC at R. What is the relation between PR and BD
2PR = BD or PR is half of BD
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Q104.
The given figure shows a parallelogram ABCD in which E is mid-point of AD and \( DL // EB\). Then, BF is equal to :
Q105.
In a parallelogram ABCD, AB = 20 cm and AD = 12 cm. The bisector of angle A meets DC at E and BC produced at F. Find the length of CF.
8 cm
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