Question

1 the following pairs of triangles are congruent, state the condition that shows they are congruent. (a) (b) (c)

Explanation:

Step1: Recall triangle congruence conditions

The main triangle congruence conditions are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side).

Step2: Analyze part (a)

In part (a), all three sides of one triangle are equal to the three sides of the other triangle. The sides are \(4\mathrm{cm}\), \(9\mathrm{cm}\), and \(12\mathrm{cm}\).
Since \(SSS\) (Side - Side - Side) congruence condition states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Step3: Analyze part (b)

In part (b), two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle. The sides are \(7\mathrm{cm}\) and \(8\mathrm{cm}\), and the included angle is \(24^{\circ}\).
Since \(SAS\) (Side - Angle - Side) congruence condition states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Step4: Analyze part (c)

In part (c), two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of the other triangle. The angles are \(40^{\circ}\), \(40^{\circ}\) and the side is \(11\mathrm{cm}\).
Since \(AAS\) (Angle - Angle - Side) congruence condition states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the triangles are congruent.

Answer:

(a) \(SSS\) (b) \(SAS\) (c) \(AAS\)