Question

Construct an
equilateral triangle of any measurement.​

Answer 1

Answer:

Step-by-step explanation:

We will be doing THREE constructions of an equilateral triangle. The first will be to construct an equilateral triangle given the length of one side, and the other two will be to construct an equilateral triangle inscribed in a circle.

METHOD 1:

Given: the length of one side of the triangle

Construct: an equilateral triangle

equiAB

STEPS:

1. Place your compass point on A and measure the distance to point B. Swing an arc of this size above (or below) the segment.

2. Without changing the span on the compass, place the compass point on B and swing the same arc, intersecting with the first arc.

3. Label the point of intersection as the third vertex of the equilateral triangle.

equiC1

See the full circles at work.

equiABcirlces

Proof of Construction: Circle A is congruent to circle B, since they were each formed using the same radius length, AB. Since AB and AC are lengths of radii of circle A, they are equal to one another. Similarly, AB and BC are radii of circle B, and are equal to one another. Therefore, AB = AC = BC by substitution (or transitive property). Since congruent segments have equal lengths, equisegmentsand ΔABC is equilateral (having three congruent sides).

Answer 2

$\large{\blue{\underline{\mathfrak{Explanation:}}}}$

_____________________________

$\large\sf{\red{Steps-of-construction:}}$

☯ Draw a line segment AB=4 cm .

☯ With A and B as centres, draw two arcs on the line segment AB and note the point as D and E.

☯ With D and E as centres, draw the arcs that cuts the previous arc respectively that forms an angle of 60° each.

☯ Now, draw the lines from A and B that are extended to meet each other at the point C.

☯ Therefore, ABC is the required triangle.

______________________________