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Determine a point which divides a line segment of length 12cm internally in the ratio of 2:3. Also, justify your construction.
CBSE | Class 10 | Constructions | Exercise 11.1 | Maths | RD Sharma
Determine a point which divides a line segment of length 12cm internally in the ratio of 2:3. Also, justify your construction.

Steps of construction:

1. Make a line segment AB=12cm by with the help of ruler.

2. Through the points A and B draw two parallel line on the opposite side of AB and making the same acute angles with the line segment.

3. Divide 2 equal parts on AX and 3 equal parts on BY such that A{{X}_{1}}={{X}_{1}}{{X}_{2}}and B{{Y}_{1}}={{Y}_{1}}{{Y}_{2}}={{Y}_{2}}{{Y}_{3}}

4.Then ,join {{X}_{2}}{{Y}_{3}}which intersects AB at P

Hence,  AP/PB=2/3.

Justification:

In \vartriangle A{{X}_{2}}Pand \vartriangle B{{Y}_{3}}P, we have

\angle AP{{X}_{2}}=\angle B{{Y}_{3}}P[vertically opposite angle]

\angle {{X}_{2}}AP=\angle {{Y}_{3}}BP[alternate interior angle]

\vartriangle A{{X}_{2}}P=\vartriangle B{{Y}_{3}}P[Because AA similarity]

\therefore AP/BP=A{{X}_{2}}/B{{Y}_{3}}=2/3[From C.P.C.T]

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