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Identifying the Angle Sum of a Triangle Theorem

Two triangles are said to be congruent if they are exactly alike. That is, they have the same side lengths and the same sized angles. There are four tests that you can use to determine if triangles are congruent. In this lesson we’ll look at two of these. First, we’ll look at test one. Test one simply states that if three sides of one triangle are exactly the same as three sides of another triangle, then they are congruent. We call this test Side Side Side or SSS.

As can be seen here each side of one triangle has been marked with a different symbol. And in the second triangle the symbols are the same, meaning they satisfy the SSS test for congruency. Let’s look at an example to clarify this a little further. In this question, we have to prove that triangle ABC is congruent to triangle DEF and then list the pairs of corresponding angles. Notice the symbol for congruency is three horizontal lines, which is an equals sign with an extra line. Let’s write down a proof to show they are congruent.

We know that AC equals FD, which equals 14 centimeters. Also CB equals FE, which equals seven centimeters. And the final pair of sides, AB and DE, is also equal, as they’re both 12 centimeters. Therefore triangle ABC is congruent to triangle DEF. Reason: SSS which stands for Side Side Side. Now if we’ve proved that the triangles are congruent we know that the triangle’s angles are also equal to each other, but now we are being asked to identify which angle in one triangle is the same as which angle in the other. In other words to name the corresponding angles. To do this we look at which vertex is opposite the corresponding equal sides.

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