Question 1 - Constrcting Line Segment in a given ratio and Similar Triangles - Constructions

Last updated at May 26, 2023 by Teachoo

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Question 1
Draw a line segment length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Give the justification of the construction.
Steps of construction:
Draw line segment AB of length 7.6 cm
Draw any ray AX,
making an acute angle with AB.
Mark 13 (= 5 + 8) points 𝐴_1, 〖 𝐴〗_2, 𝐴_3, 𝐴_4……. 𝐴_13, on AX such that 〖𝐴𝐴〗_1=𝐴_1 𝐴_2=𝐴_2 𝐴_3……. by drawing equal arcs
Join 〖𝐵𝐴〗_13.
Since we want the ratio 5 : 8,
Through point 𝐴_5 (m = 5), we draw a line parallel to 𝐴_13 𝐵
by making ∠ AA5B = ∠ AA13C
So, we copy ∠ AA13B from point A5
Note: Check how to copy an angle
from Chapter 14 Class 6
Thus, AC : CB = 5 : 8.
On measuring AC and BC by scale.
AC = 2.9 cm & BC = 4.7 cm
Justification
Since ∠ AA13B = ∠ AA5C,
So, for lines A13B and A5C, with AX as transversal,
corresponding angles are equal
∴ A13B is parallel to A5C
Now,
Since A13B is parallel to A5C,
〖𝐴𝐴〗_5/(𝐴_5 𝐴_13 )=𝐴𝐶/𝐶𝐵
(By Basic Proportionality Theorem)
By construction,
〖𝐴𝐴〗_5/(𝐴_5 𝐴_13 )= 5/8
Therefore,
𝐴𝐶/𝐶𝐵= 5/8
Thus, C divides AB in the ratio 5 : 8

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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