Compare two triangles side by side. If their angles are the same and the lengths of their sides are the same, they're congruent, which is just another way to say identical.You can flip, turn, reflect, rotate or shift one of the triangles, and they'll still be but they may not look alike. To discover if those two triangles on your geometry homework are congruent, grab your protractor, a ruler and a pencil. Get ready to do some geometrical proofs.
The Side-Side-Side (SSS) Rule
To prove two triangles are congruent using the SSS Rule, you must show that the three sides of one triangle each pair in length with one of the three sides of the second triangle. Measure the lengths of all sides of both triangles; determine whether the sides of one triangle can be matched with the sides of the other triangle.
The Side-Angle-Side (SAS) Rule
Measure the length of each side of both triangles using your ruler, and measure the angles of both triangles using your protractor. If two triangles have two sides that are the same length and one angle that is the same, you have proved they are congruent using the SAS Rule.
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The Angle-Angle-Side (AAS) Rule
Measure the length of each side of both triangles, then measure each angle. If two angles and the length of one side are the same in both triangles, you have proved the triangles are congruent using the AAS Rule.
The Right-Angle, Hypotenuse, Side (RHS) Rule
Use your protractor to measure the angles in both triangles. If each triangle contains a 90-degree angle, you have shown that both contain right angles. Use your ruler to measure the length of each hypotenuse, which is the side opposite the right angle. If the hypotenuses are the same length, then you have shown the "H" part of the RHS Rule. Measure the remaining sides of the triangles. If you find matching lengths, you have shown the triangles are congruent using the RHS Rule.