Question

1. when the base of an isosceles triangle is bisected, what type of triangle(s) are created?

one equilateral triangle
two congruent right triangles
two congruent scalene triangles
four congruent right triangles

Explanation:

1. Recall the properties of an isosceles triangle: In an isosceles triangle, the two equal sides are called the legs, and the unequal side is the base. When we bisect the base, we draw a line from the vertex opposite the base to the midpoint of the base.
2. Analyze the triangles formed: This line (the median from the apex to the base) is also the altitude and the angle bisector (by the Isosceles Triangle Theorem). So, it creates two triangles.
3. Check the type of these triangles: Each of these triangles has a right angle (since the altitude is perpendicular to the base), and they are congruent (by SAS congruence: the two legs of the original isosceles triangle are equal, the base is bisected so the two segments of the base are equal, and the included angle between the leg and the base segment is equal for both triangles). So, they are two congruent right triangles.
4. Eliminate other options:

• "One equilateral triangle" is incorrect because bisecting the base of an isosceles triangle (which is not necessarily equilateral) does not create an equilateral triangle.
• "Two congruent scalene triangles" is incorrect because the triangles formed have a right angle and two sides equal (the leg of the original isosceles triangle and the median/altitude, and the bisected base segment), so they are right triangles, not scalene.
• "Four congruent right triangles" is incorrect because bisecting the base only creates two triangles, not four.

Answer:

B. Two congruent right triangles (assuming the options are labeled as A, B, C, D with B being "Two congruent right triangles")