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Daily Review

Explore the measurement of segments PQ, determination of congruence between various segments, and the Distance Formula and Pythagorean Theorem in advanced geometry with key topics and methods explained from a 2007 lesson by Eric Hoffman at PLHS.

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Daily Review

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  1. Daily Review 1.) Find the measurement of PQ 2.) Determine whether the segments are congruent AB, GH FE, ML CD, JK AB, JK P M Q 1 ¾ in. 1 ½ in. A F G M B E H L C D J K

  2. Distance and Midpoints Eric Hoffman Advanced Geometry PLHS Aug. 2007

  3. Distance and Midpoints • Two methods of calculating distance • Distance Formula • Pythagorean Theorem • Pythagorean Theorem -

  4. Key Topics • Distance Formula – d = • The distance d between two points with coordinates (x1,y1) and (x2,y2) x -8 -4 0 4 8 12 Distance Formula.gsp

  5. Key Topics • Midpoint – the point halfway between the endpoints of a segment • The midpoint M of PQ is the point between P and Q such that PM = PQ P M Q

  6. Key Topics • Midpoint on a number line – the coordinate of the midpoint of a segment whose endpoints have coordinates A and B is A B

  7. Key Topics • Midpoint on a coordinate plane – the coordinates of the midpoint of a segment whose endpoints have coordinates (x1,y1) and (x2,y2) are ( ) Q (x2,y2) M( ) P (x1,y1)

  8. Key Topics • Segment Bisector – any line, segment, or plane that intersects a segment at its midpoint • Construction of a bisector

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