Q: How can I show that the angles are congruent without measuring the angles?

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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)

you simply cannot

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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.

Related questions

You show that they have the same measure.

the symbol for congruent is ~ with _ in the same space. (US keyboard does not have a congruent key

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)

you simply cannot

Yes. You can show this by SAS of two right triangles. Consider rectangle ABCD. AD and BC are the same length and AC and BD are the same length because opposite sides are congruent. The angles ADC and BCD are congruent since it is a rectangle and the angles are right angles. So the triangles ADC and BCD are congruent and their hypotenuses (the diagonals of the rectangles) are congruent.

Once you have shown that two triangles are congruent you can use CPCTC (corresponding parts of congruent triangles are congruent) to show the congruence of the remaining sides and angles.

Show that corresponding angles are congruent?

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Measure it, or if it is marked by a letter or number and a different shape has the SAME letter or number then the angles are congruent. A congruent angle are angles that have the same measure. Thye sign that is used to show this is ~=(~on top of the =). For example, ABC ~=PQR. This means that angle ABC has the same measure as PQR.

you can see if the top and the bottom are congruent .if they are congruent those are two parallel lineshow you can show your work.

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.