Equal Intercept Theorem

Q.

Out of the three lines AB, CD and EF, if AB is parallel to EF and CD is also parallel to EF, then what is the relation between AB and CD.

Q.

Poq is a line ray or is a perpendicular two line OS is another Ray lying between ray. op and or or prove that angle r o s=1\2(qos-pos)

Q. In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Which of the following statements is true?

1. Both (b) & (c)
2. $MN=\frac{1}{2}BC$
3. AN=NQ
4. AN = QC

Q.
In the given figure, AE||BF||CG , CD=DE and FE = 4cm. Then determine GE.

1. 8
2. 2
3. 12
4. 4

Q.

In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Which of the following statements is/are true?

1. $MN=\frac{1}{2}BC$

2. AN=NQ

3. AN = QC

4. $MN=\frac{1}{4}BC$

Q.

The adjoining figure shows a trapezium ABCD in which side AB is parallel to side DC. P and Q are mid - points of diagonals AC and BD respectively. CQ joined and produced meets AB at point R.
Which of the following options are correct?

1. PQ = $\frac{1}{4}$(AB + DC)

2. PQ = $\frac{1}{2}$(AB + DC)

3. PQ = $\frac{1}{3}$(AB -DC)

4. PQ is parallel to AB

Q.

The adjoining figure shows a trapezium ABCD in which side AB is parallel to side DC. P and Q are mid - points of diagonals AC and BD respectively. CQ joined and produced meets AB at point R.
Which of the following options are correct?

1. PQ is parallel to AB

2. Neither (a) nor (b)

3. PQ = $\frac{1}{2}$(AB - DC)

4. Both (a) and (b)

Q. In a triangle ABC, M and P are points on AB and N and Q are points on AC such that, MN || PQ || BC and AM = MP = PB. If AN = 2 cm, then NC = .

1. 2 cm
2. 4 cm
3. 6 cm

Q. In a $△ABC,D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE||BC$.
If $\frac{AD}{BD}=\frac{3}{4}$ and $AC=15cm$, find $AE$ .

Q. ABCD is a trapezium in which AB \(\parallel\) 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 ( See the given figure). Mark the correct answer option.

Q.

If l and m is interesting line and l parallel to p and m is parallel to q show that p and also intersect

Q. In the following figure, line $PY$ $\parallel$ side $BC,AP=3,PB=6,AY=5,YC=x$, then find $x$.

Q. In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Which of the following statements are true?

1. $MN=\frac{1}{2}BC$
2. AN=NQ
3. AN = QC
4. AN = NC

Q. l ll m and bisectors of l_RQB and l_DRQ intersect at P. Find the measure of l_RPQ.

Q. As shown in figure
If $l$ || $m$ || $n$ and $AB=BC$, then

1. None of these
2. $AB=QR$
3. $BC=PQ$
4. $PQ=QR$

Q. The side $AC$ of a triangle $ABC$ is produced to point $E$ so that $CE=\frac{1}{2}$ $AC$. $D$ is the mid-point point of $BC$ and $ED$ produced meets $AB$ at F and CP and DQ are parallel to AB . then $FD=\frac{1}{4}FE$ ?

1. True
2. False

Q. In triangle $ABC$; $M$ is mid-point of $AB$, $N$ is mid-point of $AC$ and $D$ is any point in base $BC$. Use intercept theorem to show that $MN$ bisects $AD$.

Q. The parallel sides of a trapezoid are $3$ cm and $9$t cm. The nonparallelsides are $4$ cm and $6$ cm. A line parallel to the base divides the trapezoidinto two trapezoids of equal perimeters. The ratio in which each of then on parallel sides is divided, if $\frac{AP}{BQ}=\frac{PD}{QC}$, is ___

1. $4:1$
2. $4:3$
3. $3:2$
4. $3:1$

Q. $s$ and $t$ are transversals cutting a set of parallel lines such that a segment of length $3$ in $s$ corresponds to a segment of length $5$ in $t.$ What is the length of segment in $t$ corresponding to a segment of length $12$ in $s?$

1. $20$
2. $\frac{36}{5}$
3. $14$
4. $\frac{5}{4}$

Q. ABCD is a quadrilateral in which AB || DC and AD || BC. A line MN, parallel to CD, is drawn meets the midpoint M of the side BC which meets AD at N. What can you say about the diagonal AC?

1. None of the above.
2. Line MN bisects AC.
3. Line AC is twice the length AD.
4. Line AC is $\frac{1}{3}$rd the length MN.

Q.

The slope of the line that is parallel to x – axis is _____.

___

Q.

In the given figure, AP = AQ and the right angles are shown. Which of the following statements can certainly be stated?

1. AB = AC

2. AP = PB

3. AQ = AD

4. None of these

Q. In the figure, lines l and m are transversals to three parallel lines AB, CD and EF. The length of AC = 12, BD = 6 and DF = 2. Find the length of CE.

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

Q.

If three or more parallel lines cut a line into equal parts, they will cut any line into ____ parts.

1. Unequal

2. Four

3. Equal

4. Three

Q. In the given figure, we have AB $\parallel$ CD $\parallel$ EF. If AB = 6 cm, CD = x BD = 4 cm and DE = y cm, calculate the value of x and y.

Q. In a $△RST$, line $l\parallel$side $ST$ and line $l$ intersects side $RS$ and side $RT$ in points $P$ and $Q$ respectively, $R-P-S$ and $R-Q-T$, then prove that $\frac{RP}{PS}=\frac{RQ}{QT}$.

Q. The side $AC$ of a triangle $ABC$ is produced to point $E$ so that $CE=\frac{1}{2}$ $AC$. $D$ is the mid-point point of $BC$ and $ED$ produced meets $AB$ at F and CP and DQ are parallel to AB .prove that $FD=\frac{1}{6}FE$ ?

1. True
2. False

Q. In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Which of the following statements is true?

1. AN=NQ
2. Both (b) & (c)
3. AN = QC
4. $MN=\frac{1}{2}BC$

Q. State whether the following statement is True or False.
The intercept theorem is also called as a basic proportionality theorem.

1. True
2. False

Q. In the given $\Delta$ ABC, M and N are mid-points of AB and AC respectively. D is any point on the base BC. Which of the following relationships will always hold true?

1. ME = EN
2. BD = DC
3. AE = ED
4. $AD=\frac{1}{2}AB$