Question

3) Draw a line segment of length 12cm and divide
at in the ratio 3:2 meausure the two parts and verify​

Answer 1

Step-by-step explanation:

ANSWER

Steps of Construction

1. Draw a line segment AB of 12cm.

2. Through the points A and B draw two parallel lines on the opposite side of AB.

3. Cut two equal parts on AX and three equal parts on BY such that AA

1

=A

1

A

2

and BB

1

=B

1

B

2

=B

2

B

3

.

4. Join A

2

B

3

which intersects AB at P.

Therefore by construction

BP

AP

=

3

2

Justification :

1. In △AA

2

P and △BB

3

P, we have

∠APA

2

=∠BPB

3

(because they are vertically opposite angles)

∠A

2

AP=∠B

3

BP (Alternate interior angles are equal)

△AA

2

P and △BB

3

P are similar to each other (Angle Angle similarity)

Therefore

BP

AP

=

BB

3

AA

2

=

3

2