Jada drew a line segment and marked its midpoint as A. With A as the center she used the compass and created a 180 degree angle by drawing an arc. She marked point B on the arc and point C to the left of point B, on the arc. She used a straightedge to connect A, B, and C.
What type of triangle did Jada construct?
An obtuse triangle, because one vertex is to the left on the arc.

An acute triangle, because all vertices are to the right on the arc.

An equilateral triangle, because the lengths of all three sides of the triangles as the same as the radius of the arc.

An isosceles triangle, because the lengths of at least two sides of the triangle are the same as the radius of the arc.

Question

Jada drew a line segment and marked its midpoint as A. With A as the center she used the compass and created a 180 degree angle by drawing an arc. She marked point B on the arc and point C to the left of point B, on the arc.  She used a straightedge to connect A, B, and C.
What type of triangle did Jada construct?
An obtuse triangle, because one vertex is to the left on the arc.
		
An acute triangle, because all vertices are to the right on the arc.
		
An equilateral triangle, because the lengths of all three sides of the triangles as the same as the radius of the arc.
		
An isosceles triangle, because the lengths of at least two sides of the triangle are the same as the radius of the arc.

directrix · Answer

An isosceles triangle, because the lengths of at least two sides of the triangle are the same as the radius of the arc.
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All points on the arc with center A are equidistant from point A. If C and B are points on that arc, then AC = AB and the triangle is isosceles. 

Note: If C and B are on the arc where the arc intersects the segment containing A, then A, B, and C are collinear in which case there is no triangle even though AC = AB.

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