Question

Construct a traingle Abc, in which Bc = 6 cm , Angle = 45 degree and Ac - Ab = 2.5 cm . Also , write the steps of construction.

Proper construction
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Answer 1

Steps of Construction :

1. Draw a line segment BC=6 cm

2. Make an angle PCB = 45∘ with the help of a protractor

3. Draw the perpendicular bisector RQ of AB

4. Draw BE⊥BP at B

Let RQ and BE intersect at O

5. Draw the circle with centre O and radius OB

Then any angle in the major segment = ∠PBC=45∘

6. Let RQ intersect BC to D is the mid-point of BC. Taking D as centre and 5 cm radius draw arcs intersecting the circle in A,A′.

7. Join AB,AC and A′B,A′C

Then the required triangle is ABC or A′BC.