2006-12-14 08:35:13 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let A and B be vertical angles. Then they are both adjacent to a third angle, C. A+C is a straight line, thus 180º, B+C is also a straight line, thus 180º. So A=180º-C=B, and by transitivity, A=B. Q.E.D.
2006-12-14 08:38:49 · answer #1 · answered by Pascal 7 · 1⤊ 0⤋
Show that one pair of adjacent angles are supplementary. Pick one of those angles and show that it is supplementary to another angle. Supplements of the same angle are congruent.
2006-12-14 08:39:41 · answer #2 · answered by bictor717 3 · 0⤊ 0⤋
this could be short and with out any symbols. Drop an altitude from the vertex of the ideal suited attitude to the hypotenuse. the two triangles formed are resembling the unique triangle and their areas sum to the unique. additionally a corresponding area of each and every of the three triangles (somewhat, each and each hypotenuse) is a facet of the unique and areas of comparable triangles are proportional to the squares of corresponding sides. by using fact the areas of the smaller 2 sum to the unique we could divide by employing the consistent of proportionality to get that the sum of the squares of the legs of the unique sq. is comparable to the sq. of the hypotenuse.
2016-12-30 10:13:29 · answer #3 · answered by dobard 3 · 0⤊ 0⤋
This is because two angles supplementary to the same angle are equal. (Why?)
Take it from there.
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Hope that helps!
2006-12-14 08:39:17 · answer #4 · answered by Anonymous · 0⤊ 0⤋