Question

how many congruent triangles are formed by connecting the midpoints of the three sides of a scalene triangle? 2 1 4 3

Explanation:

Step1: Recall the mid - point theorem

The mid - point theorem states that the line segment joining the mid - points of two sides of a triangle is parallel to the third side and half of its length.

Step2: Analyze the triangles formed

Let \(\triangle ABC\) be a scalene triangle and \(D\), \(E\), \(F\) be the mid - points of \(AB\), \(BC\), \(CA\) respectively.
By the mid - point theorem, \(DE\parallel AC\), \(DE=\frac{1}{2}AC\); \(EF\parallel AB\), \(EF = \frac{1}{2}AB\); \(FD\parallel BC\), \(FD=\frac{1}{2}BC\)
We can show that \(\triangle ADF\cong\triangle DBE\cong\triangle FEC\cong\triangle DEF\) using SSS (Side - Side - Side) congruence criterion.

Answer:

C. 4