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? ab and cb ac and bm am and cm bm and bm

Explanation:

• For the first question (midpoint definition):
• By the definition of a midpoint, a midpoint divides a line segment into two equal parts. Since \(M\) is the midpoint of \(AC\), \(AM = CM\).
• For the second question (reflexive property):
• The reflexive property states that any segment is congruent to itself. So, \(BM\cong BM\).
• For the third question (isosceles triangle definition):
• An isosceles triangle has two equal sides. In \(\triangle ABC\), \(AB\) and \(CB\) are the two equal sides.

Answer:

• Which pair of sides are congruent based on the definition of midpoint? \(AM\) and \(CM\)
• Which pair of sides are congruent based on the reflexive property? \(BM\) and \(BM\)
• Which pair of sides are congruent based on the definition of isosceles triangles? \(AB\) and \(CB\)