You would have to be given other information about the angles that would let you deduce that they are equal. For example any two right angles are equal. If two parallel lines are cut by a transversal, the alternate interior angles are equal.
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Because Corresponding Parts of Congruent Triangles, there are five ways to prove that two triangles are congruent. Show that all sides are congruent. (SSS) Show that two sides and their common angle are congruent. (SAS) Show that two angles and their common side are congruent. (ASA) Show that two angles and one of the non common sides are congruent. (AAS) Show that the hypotenuse and one leg of a right triangle are congruent. (HL)
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It depends on what is given.In general, one half of the bisected angle is proven to congruent to the other half. By the Definition of an Angle Bisector, the bisected angle can be proven bisected.---- To show that two angles are congruent:One way to prove the two angles congruent is to show that their measures are equal. This can be done if there are numbers on the diagram. Use the Protractor Postulate or the Angle Addition Postulate to find the smaller angles' measures, if they are not directly marked. Then use the Definition of Congruent Angles to prove them congruent.Given that the smaller angles correspond on a congruent or similar pair of figures in that plane and form an angle bisector, the Corresponding Parts of Congruent Figures Postulate or Corresponding Parts of Simlar Figures Postulate may be used.
To prove a trapezoid is isosceles, you need to show that the legs (the non-parallel sides) are congruent. This can be done by demonstrating that the base angles opposite these sides are congruent. You can use the triangle congruence postulates or the properties of parallel lines and transversals to establish the equality of these angles.