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How to Show Tow Triangles Are Congruent

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 that 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 congruent 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 are 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 triangles’ angles are equal to each other, but now we’re 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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