Page 3 - Lesson Note 1- ch 11 Division of line segment (Contruction)

Q. 2 Divide a line segment of length 7 cm in the ratio 2 : 4. Also prove your assertion.

Sol.

(2 marks)

Steps of Construction:
(a) Draw the line segment AB of length 7 cm.
(b) Draw any ray AX making an actue angle BAX with AB.
(c) Draw a ray BY parallel to AX by making ABY = BAX.
(d) Mark two points A1 and A2 on AX and four points B1, B2, B3 and B4 such that
AA1 = A1A2 = BB1 = B1B2 = B2B3 = B3B4.
(e) Join A2B4 which intersects AB at the point P.
Then P is the point dividing AB in the ratio 2 : 4.

Proof: Here AA2||BB4
PAA2 = PBB4 (Alternate Interior Angles)
Now, in PAA2 and PBB4
PAA2 = PBB4
APA2 = BPB4
Therefore, PAA2 ~ PBB4 by AA similarity criterion.

PA : PB = 2 : 4

Sub Topic: SIMILAR TRIANGLE

Constructing Similar Triangles

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