Question

6. Using a protractor, draw an equilateral triangle ABC (A triangle with each angle of 60° ) construct three
equal circles, with each vertex as centre. Does each circle touch the other two circles?
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Answer 1

Step-by-step explanation:

Equilateral triangles are easily constructed with a drawing compass, straightedge, and pencil because the 60⁰ interior angles can be found using only the radius of a circle around the triangle (a circumscribed circle).

Suppose you are given the length of one side of the required equilateral triangle. You must construct two identical sides that, somehow, create three interior 60⁰ angle.

Here is line segment

CE:

[insert drawing of line segment CE]

Place the needle arm of your drawing compass on

P

o

i

n

t

C

Point C, then adjust the pencil arm, so it touches

P

o

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t

E

Point E.

Swing an arc upward, making a light construction line.

Without adjusting the compass, relocate the needle to

P

o

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n

t

E

Point E.

Swing an arc upward from

P

o

i

n

t

C

Point C, making another light construction line. [insert drawing showing compass swinging arcs for these points]

Where the two arcs intersect, you have the point of an equilateral triangle's third vertex. Call it

P

o

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t

A

Point A. Use your straightedge to connect

Points A and C , Points

A

Points A andE.

You have your equilateral triangle

ACE