Question

which rule explains why these triangles are congruent?
asa
sss
sas
aas
these triangles cannot be proven congruent.
submit
work it out

Explanation:

Step1: Recall congruent triangle rules

• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides of another triangle.
• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.

Step2: Analyze the given triangles

• In \(\triangle JKH\) and \(\triangle MKH\):
• We have \(JK = MK\) (marked with one tick).
• \(\angle J=\angle M\) (marked with one arc).
• \(KH = KH\) (common side).
• This is a case of two sides (\(JK = MK\) and \(KH = KH\)) and a non - included angle (\(\angle J=\angle M\)). But wait, no! Wait, actually, if we consider the triangles \(\triangle JKH\) and \(\triangle MKH\), we have two angles (\(\angle J=\angle M\)) and a non - included side (\(KH\) is common).

Wait, no, let's re - check. The AAS (Angle - Angle - Side) congruence rule states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
In \(\triangle JKH\) and \(\triangle MKH\), \(\angle J=\angle M\) (one pair of angles), \(\angle JHK=\angle MHK\) (vertically opposite angles are equal), and \(JK = MK\) (non - included side).

Answer:

AAS