A bisector cannot bisect a line, because by definition a line is infinite. ![]() BisectorĪ bisector is an object (a line, a ray, or line segment) that cuts another object (an angle, a line segment) into two equal parts. A line is perpendicular if it intersects another line and creates right angles. Perpendicular means two line segments, rays, lines or any combination of those that meet at right angles. So 3/4‐1‐5/4 are sides of a right triangle, and 5/4 is the length of the hypotenuse.All good learning begins with vocabulary, so we will focus on the two important words of the theorem. (c) Because 5/4 is the longest length, do the following check. So are sides of a right triangle, and 5 is the length of the hypotenuse. (b) Because 5 is the longest length, do the following check. So 4‐5‐6 are not the sides of a right triangle. (a) Because 6 is the longest length, do the following check. Theorem 66: If a triangle has sides of lengths a, b, and c where c is the longest length and c 2 = a 2 + b 2, then the triangle is a right triangle with c its hypotenuse.Įxample 5: Determine if the following sets of lengths could be the sides of a right triangle: (a) 6‐5‐4, (b), (c) 3/4‐1‐5/4. The converse (reverse) of the Pythagorean Theorem is also true. Subtract x 2 + 12 x + 36 from both sides.īut x is a length, so it cannot be negative. You can also find x by using the Pythagorean Theorem.įigure 6 Using the Pythagorean Theorem to find the unknown parts of a right triangle. If you can recognize that the numbers x, 24, 26 are a multiple of the 5‐12‐13 Pythagorean triple, the answer for x is quickly found. For example, using the 3‐4‐5: 6‐8‐10, 9‐12‐15, and 15‐20‐25 are also Pythagorean triples.įigure 5 Using the Pythagorean Theorem to find a leg of a right triangle. Any multiple of one of these triples will also work. Some other values for a, b, and c that will work are 5‐12‐13 and 8‐15‐17. Therefore, 3‐4‐5 is called a Pythagorean triple. See Figure 2 for the parts of a right triangle.Įxample 1: In Figure 3, find x, the length of the hypotenuse.įigure 3 Using the Pythagorean Theorem to find the hypotenuse of a right triangle.įigure 4 Using the Pythagorean Theorem to find the hypotenuse of a right triangle.Īny three natural numbers, a, b, c, that make the sentence a 2 + b 2 = c 2 true are called a Pythagorean triple. Theorem 65 (Pythagorean Theorem): In any right triangle, the sum of the squares of the legs equals the square of the hypotenuse (leg 2 + leg 2 = hypotenuse 2). This result is known as the Pythagorean Theorem.
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