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प्रश्न
Construct a triangle ABC with side BC = 6 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are `(3)/(4)` times the corresponding sides of the ΔABC.
उत्तर
Steps of construction
(1) Draw BC = 6 cm.
(2) At point B, draw ∠XBC = 45°
(3) Using Angle Sum Property in ∆ABC,
∠A + ∠B + ∠C = 180°
105° + 45° + ∠C = 180°
∠C = 30°
And, now draw ∠YCB = 30°
(4) Now, line YC and XB intersect at point A. Thus this is our required triangle ABC.
(5) Draw an acute angle ∠CBZ at B.
(6) Now cut 4 equal arcs BB1, B1B2, B2B3, and B3B4 on BZ.
(7) Now, join B4 to C.
(8) Draw a line parallel to B4C from B3 which intersects BC at C'.
(9) Now, draw a line parallel to AC from C' which intersects BX at A'.
(10) Thus, ∆ABC is our required triangle whose sides are `(3)/(4)` times the corresponding sides of ΔABC.
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