- For A Polygon To Be Convex Means That Given Any Two Points On Or Inside The Polygon The Line Joining The Points Lies En 1 (97.32 KiB) Viewed 52 times
For a polygon to be convex means that given any two points on or inside the polygon, the line joining the points lies en
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For a polygon to be convex means that given any two points on or inside the polygon, the line joining the points lies en
For a polygon to be convex means that given any two points on orinside the polygon, the line joining the points lies entirelyinside the polygon. Use mathematical induction to prove that forevery integer n ≥ 3, the interior angles of any n-sided convexpolygon add up to 180(n − 2) degrees. Proof (by mathematicalinduction): Let P(n) be the following sentence. The interior anglesof any n-sided convex polygon add up to 180(n − 2) degrees. [Wewill show that P(n) is true for every integer n ≥ 3.] Show thatP(3) is true: P(3) is the statement that the interior angles of any-sided convex polygon add up to 180 times − 2 degrees. P(3) is truebecause any ---Select--- , and the interior angles of such apolygon add up to degrees, which equals 180 times − 2 degrees. Showthat for each integer k ≥ 3, if P(k) is true, then P(k + 1) istrue: Let k be any integer with k ≥ 3, and suppose that P(k) istrue. In other words, suppose that the interior angles of anyk-sided convex polygon add up to 180(k − 2) degrees.
For a polygon to be convex means that given any two points on or inside the polygon, the line joining the points lies entirely inside the polygon. Use mathematical induction to prove that for every integer n ≥ 3, the interior angles of any n-sided convex polygon add up to 180(n 2) degrees. Proof (by mathematical induction): Let P(n) be the following sentence. The interior angles of any n-sided convex polygon add up to 180(n − 2) degrees. [We will show that P(n) is true for every integer n ≥ 3.] Show that P(3) is true: P(3) is the statement that the interior angles of any P(3) is true because any ---Select--- " -sided convex polygon add up to 180 times and the interior angles of such a polygon add up to - 2 degrees. degrees, which equals 180 times - 2 degrees. Show that for each integer k ≥ 3, if P(k) is true, then P(k + 1) is true: Let k be any integer with k ≥ 3, and suppose that P(k) is true. In other words, suppose that the interior angles of any k-sided convex polygon add up to 180(k − 2) degrees. [This is P(k), the inductive hypothesis.]
For a polygon to be convex means that given any two points on or inside the polygon, the line joining the points lies entirely inside the polygon. Use mathematical induction to prove that for every integer n ≥ 3, the interior angles of any n-sided convex polygon add up to 180(n 2) degrees. Proof (by mathematical induction): Let P(n) be the following sentence. The interior angles of any n-sided convex polygon add up to 180(n − 2) degrees. [We will show that P(n) is true for every integer n ≥ 3.] Show that P(3) is true: P(3) is the statement that the interior angles of any P(3) is true because any ---Select--- " -sided convex polygon add up to 180 times and the interior angles of such a polygon add up to - 2 degrees. degrees, which equals 180 times - 2 degrees. Show that for each integer k ≥ 3, if P(k) is true, then P(k + 1) is true: Let k be any integer with k ≥ 3, and suppose that P(k) is true. In other words, suppose that the interior angles of any k-sided convex polygon add up to 180(k − 2) degrees. [This is P(k), the inductive hypothesis.]