Describe the steps you would take to build a triangle with an area of 15 cm2.
Answers
STEPS:
1. Place your compass point on A and measure it to 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.
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).