Construct a triangle with sides 5 cm- 6 cm and 7 cm and then another triangle whose sides are 7-5 of the corresponding sides of the first triangle-

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Constructions of Triangles

Construct a t...

Question

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

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Solution

Steps of Construction :

(i) Construct a ΔABC in which AB = 7cm, AC = 5 cm, BC = 6 cm.
(ii) At A draw an acute ΔBAX below base AB.
(iii) Along AX, mark off 7 points A₁, A₂, A₁,.,
A₇. Such that AA₁ = A₁ A₂ = A₂ A₃
= A₃A₄ =......= A₆A₇.

(iv) Join A₅B.
(v) From A₇ draw A₇B’ || A₅B meeting produced part of AB at B’.
(vi) From B’, draw B‘C’ || BC intersecting the extended line segment AC at C’.
Thus, AB‘C’ is the required triangle each of whose sides is 7/5 of the corresponding sides of the triangle ΔABC.
Justification :

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