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Here is a translation and steps to solve each problem:

Problem 1:

1. Given: \( PE = PK = PM \) and \( \angle KMP = \angle LKP \).
2. Prove: \( \triangle AMK \) is isosceles.

To solve this, use the given equal segments and angles. Show that two sides in triangle \( AMK \) are equal.

Problem 2:

1. Given: \( DE = EP = DF = MF \).
2. Prove: \( MF \) is the bisector of \( \triangle DFK \).

Apply the angle bisector theorem or verify through congruent triangles using the given equal segments.

Problem 3:

1. Given: \( EDC = 55^\circ \) and \( BEL = 24^\circ \).
2. Find: Measure of \( \angle DKL \).

Use angle properties in triangles, or the exterior angle theorem.

Problem 4:

1. Given: \( AC = BC \).
2. Find: \( \angle 3 \) if \( \angle 2 = \angle 1 = 44^\circ \).

Use isosceles triangle properties and angle sum properties to find \( \angle 3 \).

Problem 5:

1. Given: \( H \) is the height of triangle \( MNK \) and bisects \( \angle MNK \).
2. Prove: \( \triangle MNK \) is isosceles.

Use the definition of height and properties of bisector in triangles.

Grading Table:

• 7-8 points: Good
• 5-6 points: Satisfactory
• 0-4 points: Insufficient

If you need step-by-step solutions for any specific problem, let me know!