Theorem 4: Triangle and Parallelogram

Q.

What is Inradius?

1. Perpendicular distance between the incentre and any of the side of the triangle

2. Half of the length of shortest side of the triangle

3. Half of the length of longest side of the triangle

4. Perpendicular distance between incentre and and any of the vertex of the triangle

Q.

In parallelogram ABCD, if ∠A = 2x + 15^o, ∠B = 3x - 25^o, then value of x is:

1. 89^o

2. 38^o

3. 91^o

4. 34^o

Q.

If P and Q are any two points lying respectively on the sides DC and AD of a parallelogram ABCD then show that $ar\left(△APB\right)=ar\left(△BQC\right)$.

Q.

M is the midpoint of side AB of a parallelogram ABCD.If ar(AMCD) =$24c{m}^2$, find ar($△ABC)$.

Q.

ABCD is a parallelogram and EFCD is a rectangle. AL ⊥ DC, then ar(ABCD) is equal to

1. ar(∆ADL)

2. ar(∆FBC)

3. ar(EFCD)

4. ar(EALD)

Q. Question 1 (i)
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA ( see the given figure). AC is a diagonal. Show that:

SR || AC and SR = $\frac{1}{2}$AC.

Q.

In the given figure, ABCD is a parallelogram. If area $\Delta ADP=30c{m}^2$ and area $\Delta BCP=24c{m}^2,$ then area of ||gm ABCD =___ $c{m}^2$

1. 108
2. 96
3. 54
4. 27

Q. A parallelogram ABCD and a triangle ABP have a common base and are between 2 parallels. The common side is .

1. AB
2. AP
3. BP

Q.

In the given figure, ABCD is a parallelogram whose diagonals intersect at O. The areas of $\Delta AOD,\Delta DOC,\Delta COB$ and $\Delta BOA$ are $pc{m}^2,qc{m}^2,rc{m}^2$ and $sc{m}^2$ respectively. Then is the statement
$p=q\ne r=s$ true?

1. True

2. False

Q.

If the given figure is a parallelogram, find the values of x and y.

1. 29^o, 78^o

2. 23^o, 23^o

3. 29^o, 73^o

4. 23^o, 78^o

Q.

In the given figure, ABCD is a parallelogram. P and Q are midpoints of AB and AD respectively. Area $\Delta CPQ$ : Area of parallelogram ABCD is equal to

1. 3 : 5

2. 3 : 8

3. 5 : 8

4. 1 : 8

Q.

In the given figure area of parallelogram ABCD is $160c{m}^2$, then the area of $\Delta DAC$ is

1. $240c{m}^2$

2. $120c{m}^2$

3. $80c{m}^2$

4. $40c{m}^2$

Q. ABCD is a parallelogram and X and Y are the mid-points of AD and BC respectively. Which of thefollowing is not true?(1) CX trisects BD(2) AY trisects BD(3) △ ABY∼ △ CDX (4) BX is not parallel to DY

Q. Check whether the following figures are the shapes lying on the same base and between the same parallels?

Q.

In a given figure, BE is a median of $△ABD$. If the area of parallelogram ABCD is $24c{m}^2$. Then the area of $△ABE$ is:

1. 10 $c{m}^2$
2. 6 $c{m}^2$
3. 8 $c{m}^2$
4. 12 $c{m}^2$

Q.

In the given figure, ABCD is a parallelogram. E is a point in CD. AE and BC are produced to meet at F.

If area of $\Delta ADF=45c{m}^2$, then area $\Delta ABE$ =___ $c{m}^2$.

1. 22.5
2. 90
3. 45
4. 75

Q. ntABCD is a parallelogram and P is the midpoint of the side BC. Prove using vector algebra ( not by geometric process) that AC and DP meet in a common point of trisection.n

Q. The traingle QTR and the parallelogram PQSR have the same base QR and lie between _________

1. PS, QR which are not parallel
2. PS, QR which are parallel
3. PQ, SR which are parallel
4. PR, QS which are not parallel.

Q. In the given figure, ABCD and AEFD are two parallelograms.Prove that,
(i)PE=FQ?
(ii)ar(trianglePEA)=ar(triangleQFD)?
(iii)ar(triangleAPE):ar(triangleQFD):ar(trianglePFD)

Q.

PQRS and ABRS are parallelograms and X is any point on side BR. Then, ar(parallelogram PQRS) is equal to

1. ar(parallelogram ABRS)

2. ar(ΔABX)

3. ar(parallelogram ABRQ)

4. ar(quad. PSXB)

Q. O is any point in triangle ABC P, Q, R and S are the points on OA, OB, BC and AC.such that PQRS is the parallelogram and PQllAB.prove that QRllOC

Q.

In the given figure ABCD is a parallelogram. F is a point on DC and FE is the median of $\Delta ABF$. If area of $\Delta AFE$ is $15c{m}^2$, then the area of parallelogram ABCD is

1. $30c{m}^2$

2. $45c{m}^2$

3. $60c{m}^2$

4. $150c{m}^2$

Q.

In the given figure, ABCD is a parallelogram. If E AND F are midpoints of BC and AD respectively, then which of the following statements is correct?

Q. $ABCD$ is a quadrilateral in which $P,Q,R$ and $S$ are the mid-points of the sides $AB,BC,CD$ and $DA$. $AC$ is a diagonal. Show that:
i) $SR\parallel AC$ and $SR=\frac{1}{2}AC$
ii) $PQ=SR$
iii) $PQRS$ is a parallelogram.

Q.

$\Delta ABP$ and parallelogram PABC are between the same parallel lines. If the area of parallelogram PABC is $24c{m}^2$, then the area of $\Delta ABP$ is

1. $48c{m}^2$
2. $32c{m}^2$
3. $12c{m}^2$
4. $6c{m}^2$

Q. $ABCD$ is a parallelogram $P$ is a point on $AB$ such that $AP:PB=3:2$. $Q$ is a point on $CD$ such that $CQ:QD=7:3$. If $PQ$ meets $AC$ at $R$, then $AR:AC$ is

1. $1:2$
2. $6:13$
3. $5:8$
4. $4:7$

Q. $\text{In the figure, area of}\Delta DAC=45c{m}^2,\text{then find the area of rectangle ABEF in}c{m}^2.$

1. 90

Q.

In the parallelogram AMKR, KA is equal to

1. 2RK

2. RK

3. 2KS

4. KS

Q.

. If the area of || gram is 120 sq.cm , what is the ar(△) which is between the same base and same parallels?

1. 120 sq cm

2. 240 sq cm

3. 320 sq cm

4. 60 sq cm

Q. $P$ is the midpoint of side $AB$ of a parallelogram $ABCD$. A line through $B$ parallel to $PD$ meets $DC$ at $Q$ and $AD$ produced at $R$. prove that (i) $AR=2BC$
(ii) $BR=2BQ$