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Geometry Review: Pythagorean Theorem, Distance & Midpoint Formulas

This geometry review covers essential concepts including the Pythagorean Theorem, the Distance Formula, and the Midpoint Formula. Students will apply these formulas to various problems, such as identifying right triangles, calculating distances between points, and finding midpoints of line segments. Additionally, there are practical applications involving graphing points and determining the perimeter of geometric shapes. Participants should complete the exercises independently, providing answers in simplest radical form where necessary.

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Geometry Review: Pythagorean Theorem, Distance & Midpoint Formulas

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  1. Unit 2 Test Review Geometry Tuesday 9/21/10

  2. Homework Review

  3. Pre-Assessment • Answer the question on your own paper

  4. Pythagorean Theorem • Find the value of each variable. Leave your answers in simplest radical form. 1. 2. 3. 4.

  5. Pythagorean Theorem The numbers represent the lengths of the sides of a triangle. Is this a right triangle? 1. 6, 9, 10 2. 18, 24, 30 3. 20, 100, 110

  6. Distance Formula • Find the distance between the points to the nearest tenth. • 6.L(-4, 11), P(-3, 4) • 7.N(1, 0), P(3, 8) • 8. Q(10, 10), R(10, -2) • 9.S(0, 5), T(0, -3)

  7. Midpoint Formula • Find the coordinates of the midpoint of each segment. The coordinates of the endpoints are given. • 1.A(6, 7), B(4, 3) 2.C(-1, 5), D(2, -3) • 3.E(14, -2), F(7, -8) 4.G(0, 0), H(-5, 12)

  8. Midpoint Formula • 1. The midpoint of is (1, 2). The coordinates of A are (-3, 6). Find the coordinates of B. • 2. The midpoint of is (4, 11). The coordinates of D are (4, 12). Find the coordinates of C. • 3. The midpoint of is (-3, 7). The coordinates of E are (-3, 10). Find the coordinates of F.

  9. Applications • 1. Graph the points and .Draw the segments connecting A,B,C, and D in order. Are the lengths of the sides of ABCD the same? Explain. •  2. A crow flies to a point that is 1 mile east and 20 miles south of its starting point. How far does the crow fly?

  10. Applications • Quadrilateral PQSRhas coordinates as follows: P(0, 0), Q(-1, 4),R(8, 2), and S(7, 6). • 1. Graph quadrilateral PQSR. • 2. What is the perimeter of PQSR? • 3. What is the midpoint of QR?

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