Construct a triangle ABC in which BC is 8 cm- - B is 70- and AB - AC - 7- -4 MARKS-

Steps : 1 Mark Construction : 3 Marks Steps: nbsp; 1. nbsp;Draw line segment BC = 8cm. Draw ray BX which makes an angle 70^∘ nbsp;with BC. 2. nbsp;Cut ...

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Standard IX

Mathematics

Construction of Perpendicular Bisector and its Proof

Construct a t...

Question

Construct a triangle ABC in which BC is 8 cm, $∠$ B is $70^{\circ}$ and AB - AC = 7. [4 MARKS]

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Solution

Steps : 1 Mark
Construction : 3 Marks

Steps:
1. Draw line segment BC = 8cm. Draw ray BX which makes an angle $70^{\circ}$ with BC.

2. Cut off line segment BD of length AB - AC = 7 on BX. Join CD.

$N O T E : A s p o i n t B c o n t a i n s s i d e A B w h i c h i s g r e a t e r t h a n s i d e A C h e n c e w e c u t o f f l i n e s e g m e n t B D = 7 c m (w h i c h e q u a l s A B - A C = 7 c m) o n t h e s a m e s i d e o f B X$

3. Draw the perpendicular bisector of CD. Let the perpendicular bisector intersect ray BX at A.

4. Triangle ABC is the required triangle.

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Construct a triangle ABC in which BC is 8 cm, ∠ B is 70∘ and AB - AC = 7. [4 MARKS]

Construct a triangle ABC in which BC is 8 cm, $∠$ B is $70^{\circ}$ and AB - AC = 7. [4 MARKS]