![]() You have two right triangles, ABC and RST. Then it's just a matter of using the SSS Postulate.įigure 12.8 illustrates this situation. If you use the Pythagorean Theorem, you can show that the other legs of the right triangles must also be congruent. Not to mention the fact that a SSA relationship between two triangles is not enough to guarantee that they are congruent. Your plate is so full with initialized theorems that you're out of room. There are several ways to prove this problem, but none of them involve using an SSA Theorem. If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent. Theorem 12.3: The HL Theorem for Right Triangles.Now it's time to make use of the Pythagorean Theorem. You've made use of the perpendicularity of the legs in the last two proofs you wrote on your own. ![]() Finally, you know that the two legs of the triangle are perpendicular to each other. You also have the Pythagorean Theorem that you can apply at will. since we know that all angles in a triangle add up to 180 degrees, 50 + 70 120 and 180 - 120 60, leaving us with 50, 70, and 60 degree angles in both triangles. ex: both mno and pqr have angles 50, 70, and x degrees. For example, not only do you know that one of the angles of the triangle is a right angle, but you know that the other two angles must be acute angles. aas: if two angles are the same on both triangles, then the third angle will be the same and they will be congruent. Whenever you are given a right triangle, you have lots of tools to use to pick out important information. Then you'll have two angles and the included side of ABC congruent to two angles and the included side of RST, and you're home free.ĪBC and RST with A ~= R, C ~= T, and ¯BC ~= ¯ST. But wait a minute! Because the measures of the interiorangles of a triangle add up to 180º, and you know two of the angles in are congruent to two of the angles in RST, you can show that the third angle of ABC is congruent to the third angle in RST. If only you knew about two angles and the included side! Then you would be able to use the ASA Postulate to conclude that ABC ~= RST. Given: Two triangles, ABC and RST, with A ~= R, C ~= T, and ¯BC ~= ¯ST.Figure 12.7 Two angles and a nonincluded side of ABC are congruent to two angles and a nonincluded side of RST.
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