Question

a side - side - side congruent triangle theorem
b side - angle - side congruent triangle theorem
c angle - angle - side congruent triangle theorem
d angle - side - angle congruent triangle theorem
e hypotenuse leg congruent triangle theorem
f not congruent

Explanation:

Step1: Identify the congruent sides

From the figure, we have \(FJ = FG\) (one pair of equal sides), \(JH=GH\) (another pair of equal sides), and \(FH = FH\) (common side, the third pair of equal sides).

Step2: Apply the congruent triangle theorem

The Side - Side - Side (SSS) Congruent Triangle Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent. Here, in \(\triangle FJH\) and \(\triangle FGH\), since \(FJ = FG\), \(JH = GH\), and \(FH=FH\), we can use the SSS theorem.

Answer:

A. Side - Side - Side Congruent Triangle Theorem