Name: Division of Line Segment in Given Ratio Externally
Uploaded: 2019-07-19
Duration: 5 min 53 s
Description: Line segments can also be divided by a point, not on the line. In this video, you will learn how to divide a line segment externally in some ratio, using a r...

Question

Anoara drew a triangle

A B C

in her exercise book. We bisect side

B C

by compass and then draw the median

A D

. I trisect

A D

in

A E, E F and F D

. Now we join

B

and

F

by scale and extended it to

X

such that it intersect

A C

at

X

. Measuring by scale we see,

A X =

_____

C X

(Let's put the number)

Accepted Answer

Step1: Draw a $Δ A B C$ of any length with a scale.

Now we will bisect $B C$ and mark the centre as $D$ .

Step2: Take any distance in compass approximately greater than half of $B C$ . Keep the needle of the compass on point $B$ and mark arcs above and below $B C$ .

Step3: Keeping the distance in the compass the same as that of in step2 keep the needle of the compass on point $C$ and intersect arcs drawn in step2. Join their intersection points. Mark the intersection of the line with $B C$ as $D$ and join $A D$ . $A D$ is the median.

Now we have to trisect the median $A D$ that is we have to divide the median in $3$ equal parts.

In the first step when dividing a line into equal parts we draw a ray at any angle to the given line. Here the line which we have to divide is $A D$ . Let $A B$ be the ray.

Step4: Take any distance in compass and keep the needle of the compass on point $A$ and draw an arc intersecting $A B$ . Name the intersection point as $X_{1}$ . keeping the distance the same in compass keep the needle on point $X_{1}$ and mark an arc intersecting $A B$ at $X_{2}$ . Draw $3$ such parts that is upto $X_{3} .$ By doing this we are making $3$ equal parts on the $A B$ .

Step5: Join $X_{3}$ and $D$ and draw parallels to $D X_{3}$ from $X_{2} and X_{1}$ which intersects $A D$ at $F and E$ respectively.

Thus we have divided $A D$ in $3$ equal parts $A E, E F and F D$ .

Step6: Draw a line passing through points $B and F$ and let it intersect $A C$ at $X$

Measure $A X and X C$ using scale both are equal

$A X = C X$

Hence, the blank should be filled with $1$ .

$\Rightarrow A X = 1 \times C X$

Important Questions on Dividing a Line Segment Into Three or Five Equal Parts

Learn and Prepare for any exam you want !

Anoara drew a triangle ABC in her exercise book. We bisect side BC by compass and then draw the median AD. I trisect AD in AE, EF and FD. Now we join B and F by scale and extended it to X such that it intersect AC at X. Measuring by scale we see, AX=_____ CX (Let's put the number)

Important Questions on Dividing a Line Segment Into Three or Five Equal Parts

Learn and Prepare for any exam you want !