Question

if necessary, you may learn what the markings on a figure indicate. (a) not necessarily congruent congruent: △ghi≅△□ by the (b) not necessarily congruent congruent: △abc≅△□ by the (c) not necessarily congruent congruent: △mno≅△□ by the

Explanation:

Step1: Analyze (a)

In \(\triangle GHI\) and \(\triangle JHI\), \(\angle G=\angle J = 90^{\circ}\), \(HI = HI\) (common side), \(\angle GIH=\angle JIH\) (given). By the AAS (Angle - Angle - Side) congruence criterion, \(\triangle GHI\cong\triangle JHI\).

Step2: Analyze (b)

In \(\triangle ABC\) and \(\triangle DEF\), \(AB = DE\), \(BC = EF\), \(AC = DF\). By the SSS (Side - Side - Side) congruence criterion, \(\triangle ABC\cong\triangle DEF\).

Step3: Analyze (c)

In \(\triangle MNO\) and \(\triangle PRQ\), the side - side - angle (SSA) condition is given. SSA does not guarantee triangle congruence. So \(\triangle MNO\) and \(\triangle PRQ\) are not necessarily congruent.

Answer:

(a) Congruent: \(\triangle GHI\cong\triangle JHI\) by the AAS (Angle - Angle - Side) criterion.
(b) Congruent: \(\triangle ABC\cong\triangle DEF\) by the SSS (Side - Side - Side) criterion.
(c) Not Necessarily Congruent.