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To construct a triangle in which …

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To construct a triangle in which ab equals to 6 CM angle equals to 30 and angle B equals to 60 degree construct another triangle A B dash dash similar to triangle a triangle ABC with base ab is equals to 8 cm

Posted by Dhruva Gupta 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Construction:

Steps of construction:

Draw a line segment {tex}AB = 6 \ cm.{/tex}
At A, construct {tex}\angle{/tex}{tex}BAZ{/tex} = {tex}30 ^ { \circ }{/tex} and at B, construct {tex}\angle{/tex}{tex}ABY {/tex}= {tex}60 ^ { \circ }{/tex}
Suppose AZ and BY intersect at C.
{tex}\triangle{/tex}{tex}ABC {/tex} so obtained is the given triangle.
Below AB, make an acute {tex}\angle{/tex}BAX.
Along AX, mark off 8 points {tex}B_1, B_2, B_3, B_4, B_5, B_6, B_7, B_8{/tex}
such that {tex}AB_1 = B_1B_2 = B_2B_3 = B_3B_4 = B_4B_5 = B_5B_6 = B_6B_7 = B_7B_8{/tex}
Join B₆B.
From B₈, draw {tex}B_8B'||B_6B {/tex} meeting AB produced at B'.
From B', draw B'C'{tex}\|{/tex}BC, meeting AZ at C'.
Thus, {tex}\triangle{/tex}AB'C' is the required similar triangle.

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