Answered: You can use the Pythagorean Theorem to…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter9: Real Numbers And Right Triangles

Section9.5: The Distance And Midpoint Formulas

Problem 51E

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Question

You can use the Pythagorean Theorem to prove the Distance Formula. Let points P(x1, y1 ) and Q(x2 , y2) be the endpoints of the hypotenuse of a right triangle.

a. Write an algebraic expression to complete each of the following: PR = ? and QR = ? .

b. By the Pythagorean Theorem, PQ squared = PR squared + QR squared . Rewrite this statement by substituting the algebraic expressions you found for PR and QR in part (a)

c. Complete the proof by taking the square root of each side of the equation that you wrote in part (b).

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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