Question

determine if each pair of triangles are congruent. if they are label it with the correct postulate. if they are not congruent, then use
ot possible.\

Explanation:

6.

• Identify congruent parts:
• In triangles \( \triangle JKM\) and \( \triangle LMK\), \(JK = LM\) (given by marks), \(KM=MK\) (common side), \(\angle JMK=\angle LKM\) (given angles).
• Apply congruence postulate:
• By the Side - Angle - Side (SAS) postulate, \(\triangle JKM\cong\triangle LMK\).

7.

• Identify congruent parts:
• In triangles \( \triangle ABC\) and \( \triangle DEC\), \(BC = DC\) (given by marks), \(\angle ACB=\angle ECD\) (vertical angles), \(AC = EC\) (given by marks).
• Apply congruence postulate:
• By the Side - Angle - Side (SAS) postulate, \(\triangle ABC\cong\triangle DEC\).

8.

• Identify congruent parts:
• In triangles \( \triangle FGG\) and \( \triangle HGG\) (assuming \(G\) is the vertex), \(\angle FGG=\angle HGG\) (given angles), \(GG = GG\) (common side), \(\angle FGG=\angle HGG\) (given angles).
• Apply congruence postulate:
• By the Angle - Side - Angle (ASA) postulate, \(\triangle FGG\cong\triangle HGG\).

9.

• Identify congruent parts:
• In right - triangles \( \triangle PSR\) and \( \triangle PQR\), \(PS = PQ\) (given by marks), \(PR = PR\) (common side).
• Apply congruence postulate:
• By the Hypotenuse - Leg (HL) postulate (since they are right - triangles), \(\triangle PSR\cong\triangle PQR\).

10.

• Identify congruent parts:
• In triangles \( \triangle SRT\) and \( \triangle RUS\), \(SR = RU\) (given by marks), \(ST = UR\) (given by marks), \(SU=SU\) (common side).
• Check congruence:
• The sides do not satisfy any congruence postulate (SSS, SAS, ASA, AAS, HL). So, it is not possible.

11.

• Identify congruent parts:
• In triangles \( \triangle ABC\) and \( \triangle DEC\), \(AB = DE\) (given by marks), \(BC = DC\) (given by marks), \(AC = EC\) (given by marks).
• Apply congruence postulate:
• By the Side - Side - Side (SSS) postulate, \(\triangle ABC\cong\triangle DEC\).

Answer:

1. \(\triangle JKM\cong\triangle LMK\) (SAS)
2. \(\triangle ABC\cong\triangle DEC\) (SAS)
3. \(\triangle FGG\cong\triangle HGG\) (ASA)
4. \(\triangle PSR\cong\triangle PQR\) (HL)
5. Not Possible
6. \(\triangle ABC\cong\triangle DEC\) (SSS)