Question

isosceles triangle abc is folded along bm with m chosen in such a way that it is the midpoint of side ac, the shortest side. which pair of sides are congruent based on the definition of midpoint? which pair of sides are congruent based on the reflexive property? which pair of sides are congruent based on the definition of isosceles triangles?

Explanation:

• Based on the definition of midpoint: The midpoint \(M\) of side \(AC\) divides \(AC\) into two equal - length segments. By the definition of a midpoint (\(M\) is a point on \(AC\) such that \(AM = MC\)).
• Based on the reflexive property: The reflexive property of congruence states that any geometric figure is congruent to itself. For the line segment \(BM\), \(BM\cong BM\) (a segment is congruent to itself).
• Based on the definition of isosceles triangles: An isosceles triangle has two sides of equal length. In \(\triangle ABC\), by the definition of an isosceles triangle, \(AB = BC\).

Answer:

• \(AM\) and \(MC\)
• \(BM\) and \(BM\)
• \(AB\) and \(BC\)