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MODULE I VOCABULARY PART II

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FIGURE IT OUT! The first new term we will discuss is distance. Distance a measurement of the length of how far something is through space.

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FIGURE IT OUT! Much of what we do with distances will involve coordinates. How far is it between these two coordinates?

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FIGURE IT OUT! How about these two?

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FIGURE IT OUT! What about these?

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FIGURE IT OUT! When two points aren’t directly next to, or above each other, we can use the distance formula to see how far apart they are.

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FIGURE IT OUT! The distance formula is really just the Pythagorean Theorem which is a² + b² = c².

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FIGURE IT OUT! “a” represents one leg of the triangle and “b” represents the other. “c” represents the hypotenuse. a b c

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FIGURE IT OUT! Now in this case, a = 3 and b = 4. I don’t know c yet, so it stays c for now. 3 4 c

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FIGURE IT OUT! When we plug our a and b value into the Pythagorean Theorem we get 3² + 4² = c² or 9 + 16 = c². That equals 25 = c² So c = 5 3 4 5

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FIGURE IT OUT! But sometimes we won’t be given a picture! Sometime we are just given the points. How far is it between (5, 2) and (2, 6)? For that, we need the distance formula.

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FIGURE IT OUT! The distance formula is … (x 2 – x 1 )² + (y 2 – y 1 )² = D² Do you see how that is similar to the Pythagorean Theorem?

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FIGURE IT OUT! We have to first pick our x 2, x 1, y 2, and y 1. (5, 2) and (2, 6) It doesn’t matter which you pick as long as you stay consistent throughout the problem. x 1 y 1 x 2 y 2

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FIGURE IT OUT! (2 – 5)² + (6 – 2)² = D² is therefore our new equation. (-3)² + (4)² = D² 9 + 16 = D² 25 = D² 5 = D

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FIGURE IT OUT! Next, we have an angle. An angle is two rays extending from a common endpoint called the vertex. These are measured in degrees. When an angle has a measure of 90⁰ we call that a right angle.

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FIGURE IT OUT! To measure an angle, you line up the notch of a protractor with the vertex and line up one ray with the zero on the protractor. Wherever the other ray is pointing, that’s the degree of the angle.

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FIGURE IT OUT! A circle is the set of all points in a plane equidistant to a given point called a center. The circumference of the circle is the length around the outside. An arc is part of the circumference of a circle, or part of any curve.

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FIGURE IT OUT! When one thing is the same distance from two different things we say that it is equidistant from them. When two things cross over each other, we say they intersect.

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FIGURE IT OUT! Lastly, we’ll begin our discussion of conditional statements. Conditional statements are statements of the if-then form where the if something happens, then another thing happens.

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FIGURE IT OUT! If an animal is a Labrador, then it is a dog. – Real or not real? If an animal is a dog, then it is a Labrador. – Real or not real?

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Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

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