construction a equatorial triangle with steps
Answers
Answer:
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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).