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:
• We have \(JK = ML\) (marked as equal), \(\angle JKM=\angle LMK\) (given angles), and \(KM = MK\) (common side).
• Apply congruence postulate:
• By the Angle - Side - Angle (ASA) postulate, \(\triangle JKM\cong\triangle MLK\).

7.

• Identify congruent parts:
• \(\angle A=\angle D\) (given angles), \(AC = DC\) (vertical angles are equal, \(\angle BCA=\angle ECD\)), and \(AB = DE\) (marked as equal).
• Apply congruence postulate:
• By the Angle - Angle - Side (AAS) postulate, \(\triangle ABC\cong\triangle DEC\).

8.

• Identify congruent parts:
• \(\angle F=\angle H\) (since \(\angle FGI+\angle IGH=\angle HGI +\angle IGH\) and \(\angle FIG=\angle HIG = 90^{\circ}\)), \(GI = GI\) (common side), \(\angle FIG=\angle HIG\) (right angles).
• Apply congruence postulate:
• By the Angle - Angle - Side (AAS) postulate, \(\triangle FGI\cong\triangle HGI\).

9.

• Identify congruent parts:
• \(PS = PQ\) (marked as equal), \(PR = PR\) (common side), \(\angle PRS=\angle PRQ = 90^{\circ}\).
• Apply congruence postulate:
• By the Hypotenuse - Leg (HL) postulate (for right - angled triangles), \(\triangle PRS\cong\triangle PRQ\).

10.

• Identify congruent parts:
• \(SR

eq TU\), \(ST
eq RU\) (marked with different number of ticks).

• Determine congruence:
• Not all corresponding sides are equal. So, it is not possible to prove the triangles \(\triangle SRU\) and \(\triangle TUS\) congruent.

11.

• Identify congruent parts:
• \(AB = DE\) (marked as equal), \(BC = EC\) (marked as equal), \(AC = DC\) (marked as equal).
• Apply congruence postulate:
• By the Side - Side - Side (SSS) postulate, \(\triangle ABC\cong\triangle DEC\).

Answer:

1. \(\triangle JKM\cong\triangle MLK\) (ASA)
2. \(\triangle ABC\cong\triangle DEC\) (AAS)
3. \(\triangle FGI\cong\triangle HGI\) (AAS)
4. \(\triangle PRS\cong\triangle PRQ\) (HL)
5. Not Possible
6. \(\triangle ABC\cong\triangle DEC\) (SSS)