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:

Step1: Mid - point definition

If \(M\) is the mid - point of \(AC\), by the definition of a mid - point (\(M\) divides \(AC\) into two equal parts), \(AM = CM\).

Step2: Reflexive property

The reflexive property of congruence states that any geometric figure is congruent to itself. So, \(BM\cong BM\).

Step3: Isosceles triangle definition

An isosceles triangle has two equal sides. In \(\triangle ABC\), by the definition of an isosceles triangle, \(AB = CB\).

Answer:

• First question: AM and CM
• Second question: BM and BM
• Third question: AB and CB