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How to Prove Triangles Are Congruent in Geometry

Every triangle has three sides connected by three angles. When triangles have the same basic shape, the sides and angles from each in the same position are said to be corresponding; when triangles have the same measurements for those corresponding sides and angles, the triangles are congruent. To prove that a triangle is congruent to another, you do not have to know all of the measurements of both triangles, just key ones. You can prove that triangles are congruent with different combinations of specific corresponding sides and angles.

Things You'll Need

  • Ruler
  • Protractor
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Instructions

    • 1

      Measure the hypotenuses and a corresponding side of each triangle if they are right triangles. A right triangle is a triangle that possesses one 90-degree angle and its hypotenuse is the side opposite the right angle. If the hypotenuses' and the corresponding sides' lengths are equal, then the triangles are congruent.

    • 2

      Measure the right triangles' hypotenuse and a corresponding angle other than their right angles. If the hypotenuses' length and the corresponding angles' measurements are equal, then the triangles are congruent.

    • 3

      Measure all three sides of each triangle. If each side of one triangle has the same length as the corresponding side of the other, then the triangles are congruent.

    • 4

      Select and measure two corresponding angles and a side that connects them from each triangle. If the corresponding angle measurements and the side lengths are equal, then the triangles are congruent.

    • 5

      Select and measure two corresponding angles and a corresponding side length that is not between the two angles. If the corresponding angle and side measurements are equal, then the triangles are congruent.

    • 6

      Select and measure two corresponding adjacent sides and the angle that forms between them from each triangle. If the corresponding side and angle measurements are equal, then the triangles are congruent.

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