Question

draw an equilateral triangle of side 6cm draw it's altitudes are they equal?




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Answer 1

Answer:

Data: To Construct an equilateral triangle, given its side.

Steps of Construction :

1. Construct AB = 6 cm.

2. With A as centre and convenient scale draw an arc, it meets AB at P.

3. With P as centre, with same radius draw an arc, it intersects first arc at Q, AQ is joined and produced ∠QAB=60

0

.

4. With A as centre and taking 6cm radius draw an arc. It intersects at C which is produced line of AQ.

5. Next, BC is joined, ABC is an equilateral triangle.

In △ABC, ∠A=∠B=∠C=60

0

AB = BC = CA = 6 cm.

In △ABC, AB=AC=6cm. ∠A=60

0

∠B=60

0

∠A+∠B+∠C=180

0

60+∠B+∠B=180(∵∠B=∠C)

60+2∠B=180

2∠B=180−60

2∠B=120

0

∠B=

2

120

=60

0

∴∠B=∠C=60

0

∴∠A=∠B=∠C=60

0

AC = BC (Opposite sides of equal angles)

But, AB = AC (known)

∴ AB= BC = CA = 6 cm.