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Standard IX

Mathematics

Proof for Validity of Construction of an Angle of 60 Degrees

Which of the ...

Question

Which of the following can be constructed using the following steps?

Step1:Put the tip of the compass at point A

Step 2: Open the compass so that pencil tip is at point B.

Step 3: Draw an arc above AB.

Step 4: Without changing the opening, put the metal tip on point B and draw an arc intersecting the first arc at point C.

Step 5: Draw AC and BC.

Right angle triangle

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Obtuse angle triangle

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Scalene triangle

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Equilateral triangle

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Solution

The correct option is D
Equilateral triangle

When you measured the angles of triangle, all are same having value as 60 $^{\circ}$

So, $Δ$ ABC is an equilateral triangle.

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Similar questions

If I do the following constructions step by step, what will be the angles constructed (in degrees)?

Step 1. Draw an arc on the line XY with an arbitrary point O on line XY, as centre and radius r. With the same radius and point of intersection of arc and line, ‘A’, as centre draw another arc on the first arc at point B. So, $∠ A O B$ is __.

Q. Which of the following step is not required to construct a

△ A B C

, when AB = 7.6 cm, AC = 6 cm and CB = 4 cm.

Q. The steps of construction of an

∠ A O B = 45^{o}

is given in jumbled order below:
1. Place compass on intersection point.
2. Place ruler on start point and where arc intersects perpendicular line.
3. Adjust compass width to reach start point.
4. Construct a perpendicular line.
5. Draw

45

degree line.
6. Draw an arc that intersects perpendicular line.
Which step comes first?

Length of sides of a

△ A B C

A B = 5 c m

A C = 3 c m

and

B C = 4 c m

. Then, construct the triangle formed by these three sides by following these steps. Put them in proper order.

Step 1. Draw a line segment

A B = 5 c m

Step 2. Now assuming

B

as centre draw an arc of

4 c m

intersecting the previous arc at

C

Step 3. Assuming

A

a centre draw an arc of radius

3 c m

Step 4. Now join

A

C

and

B

C

Q. Length of sides of a

△ A B C

A B = 5 c m

A C = 3 c m

and

B C = 4 c m

. If the construction of the triangle formed by these three sides include following steps, then answer the following question:

Which of the following is the first step of construction?

Steps of construction:

Step 1. Now join

A

C

and

B

C

Step 2. Assuming

A

a centre draw an arc of radius

3 c m

Step 3. Now assuming

B

as centre draw an arc of

4 c m

intersecting the previous arc at

C

Step 4. Draw a line segment

A B = 5 c m

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The correct option is D Equilateral triangle When you measured the angles of triangle, all are same having value as 60∘​ So, Δ ABC is an equilateral triangle.

The correct option is D
Equilateral triangle

When you measured the angles of triangle, all are same having value as 60 $^{\circ}$

So, $Δ$ ABC is an equilateral triangle.