Converse of Theorem 2

Q. Prove that parallelogram on the same base and between the same parallels are equal in area.

Q.

A parallelogram and a triangle are on equal bases and between the same parallel lines. The ratio of their areas is 2:1

1. 1 : 1

2. 1 : 2

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 figure formed by joining the mid-points of the adjacent sides of a parallelogram is a

(a) rectangle

(b) parallelogram

(c) rhombus

(d) square

Q.

In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that

(i) area (PQRS) $=$ area (ABRS)

(ii) area (AXS) $=\frac{1}{2}$ area (PQRS)

Q.

ABCD is a parallelogram, Area(DAB)=

1. 1/2 [Ar (||^gmABCD)]

2. 1/4 [Ar (||^gmABCD)]

3. 3/4 [Ar (||^gmABCD)]

4. 2A(||^gmABCD)

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. $Noneofthese$

Q. A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Then,

1. $Area\left(\Delta ABCD\right)=Area\left(\Delta ACF\right)$
2. $Area\left(\Delta ADF\right)=Area\left(\Delta ABFC\right)$
3. $Area\left(\Delta ABF\right)=Area\left(\Delta ACF\right)$
4. $Noneofthese$

Q. ______ is not a parallelogram.

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

Q.

In ∆ triangle ABC, D and E are the midpoints of side AB and AC. State which of the following are correct option(s).

1. Area of ∆BEC and ∆ BDC are equal.

2. (1/2)Area of BDEC = Area of ∆BDC

3. DE is parallel to BC

4. All of the above

Q. In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={50}^{\circ }$, then $\angle CAO$ is equal to__.

1. ${30}^{\circ }$
2. ${40}^{\circ }$
3. ${50}^{\circ }$
4. ${60}^{\circ }$

Q.

In ∆ABC, if L and M are points on AB and AC respectively such that LM || BC then ar (LMC) is equal to

1. ar (MBC)

2. ¹/₂ ar (LBM)

3. ar (LOB)

4. ar (LBM)

Q. The line drawn through the centre of a circle. Which of the following is correct about the line drawn?

1. Line is parallel to chord
2. Line is perpendicular to chord
3. Line is collinear with chord
4. Line is equal to diameter

Q.

If AD is the median of a triangle ABC and area of triangle $ADC=15c{m}^2$, then $\frac{ar\left(\Delta ABC\right)}{15}=$ ____.

1. $\frac{9}{3}c{m}^2$

2. $4c{m}^2$

3. $\frac{16}{4}c{m}^2$

4. $2c{m}^2$

Q. 12 ABCD is a ||gm, G is apoint on AB such that AG=2GB, E is a point on DC such that CE=2DE and F is a point of BC such that BF=2FC: Prove that : 1. ar triangleEBG=ar triangle EFC 2. Find what proportion of the area of parallelogram is the are of EFG

Q. ABCD is a trapezium with AB//DC. A line parallel to AC intersects AB at point M and BC at point N. Prove that: Area of triangle ADM = Area of triangle ACN.

Q.

In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that

(i) ar (ACB) = ar (ACF)

(ii) ar (AEDF) = ar (ABCDE)

Q.

In the given figure ABCD is a parallelogram. If area of parallelogram ABCD = 708 square units, then what is the area of $\Delta BEC$?

Q. Equal chords are equidistant from the centre of circle.

1. False
2. True

Q. 47. If a number of circles touch a given line segment PQ at a point A then prove that their centres lie on the perpendicular of PQ but dont lie on the bisector or PQ

Q. Choose the incorrect statements among the following given options.

1. The area of a triangle is half the product of any of its sides and the corresponding altitude
2. The area of a trapezium is half the product of its height and the sum of the parallel sides
3. Area of a parallelogram is the product of any of its sides and the corresponding altitude
4. A diagonal of a parallelogram divides it into two triangles of distinct areas

Q.

A parallelogram and a triangle are on equal bases and between the same parallel lines. The ratio of the area of parallelogram : area of triangle is 2:1.

1. 1 : 1

2. 1 : 2

Q. Statement 1: Things which coincide with one another may or may not be equal to one another.
Statement 2 :Things which are double of the same things are equal to one another.
Choose the correct option(s) from the following :

1. Statement $1$ is right
2. Statement $2$ is right
3. Statement $1$ is wrong
4. Statement $2$ is wrong

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. $ABC$ is a right angled triangle, right angled at $B$ such that $BC=6$ cm and $AB=8$ cm. A circle with centre $O$ is inscribed in $△ABC$. The radius of the circle is

1. $1$ cm
2. $2$ cm
3. $3$ cm
4. $4$ cm

Q.

In the figure, EF $\parallel$ AB and E is the mid-point of FG. Find the ratio of area (ABCDO) to the sum of area (BAFGO) and area (AEB).

1. 1 : 1

2. 1 : 2

3. 2 : 1

4. 1 : 3

Q. The medians of a triangle $ABC$ intersect each other at point $G$ . If one of its medians is $AD$ .prove that Area $(△BGC)=\frac{1}{3}\times$ Area $(△ABC)$

Q. A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is

(a) 1 : 1

(b) 1 : 2

(c) 2 : 1

(d) 1 : 3

Q.

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).

Q. In the given figure, AD and CD are the chords of the circle with centre 'O'. If AD = CD, ∠AOB = 60° and ∠BOC = 30°, then find ∠ADC.