![]() ![]() ![]() I hope that this isn't too late and that my explanation has helped rather than made things more confusing. If two numbers b and c have the property that their difference b-c is integrally divisible by a number m (i.e., (b-c)/m is an integer), then b and c are said to be 'congruent modulo m.' The number m is called the modulus, and the statement 'b is congruent to c (modulo m)' is written mathematically as bc (mod m). You can then equate these ratios and solve for the unknown side, RT. Meaning of Congruent If two figures can be placed precisely over each other, they are said to be ‘congruent’ figures. ![]() If you want to know how this relates to the disjointed explanation above, 30/12 is like the ratio of the two known side lengths, and the other ratio would be RT/8. Now that we know the scale factor we can multiply 8 by it and get the length of RT: Congruence can be applied to line segments, angles, and figures. The angles are consecutive and corresponding in nature while the sides are not included between the angles but in either direction of the angles. In geometry, congruent figures are shapes that can be transformed into one another through rotations, reflections, or translations. In geometry, congruent means identical in shape and size. If you solve it algebraically (30/12) you get: By definition, AAS congruence rule states that if any two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle. I like to figure out the equation by saying it in my head then writing it out: In this case you have to find the scale factor from 12 to 30 (what you have to multiply 12 by to get to 30), so that you can multiply 8 by the same number to get to the length of RT. The first step is always to find the scale factor: the number you multiply the length of one side by to get the length of the corresponding side in the other triangle (assuming of course that the triangles are congruent). ![]()
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