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Concept Review

This lesson focuses on essential geometric concepts, including congruent segments and angles, midpoints, and bisectors. Students will learn that two segments are congruent if they have the same measure, and that a midpoint divides a segment into two equal parts. The lesson covers the definition and function of segment and angle bisectors, as well as the concept of perpendicular lines. Additionally, the Distance Formula is introduced for finding the distance between points in a coordinate plane, solidifying foundational skills necessary for advanced geometry study.

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Concept Review

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  1. Concept Review

  2. 2.3 Segment and Angle Relationships It is vital in this course that each word we study becomes part of your geometric vocabulary.Two segments are congruent, AB  CD, if they have the same measure. Two angles are congruent, <P  <Q, if they have the same measure. Q A B D C P AB = CD m<P = m<Q

  3. The midpoint of a segment is the point that divides the segment into two congruent segments. R S T(S is the midpoint) RS = ST

  4. A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint. An angle bisector is a ray that divides the angle into two congruent angles. G S R T I O H RS = ST m<HOI = m<IOG

  5. Two lines are perpendicular if they intersect to form a right angle. A line is perpendicular to a plane if it is perpendicular to each line in the plane that intersects it. l l m P l P l m

  6. The Distance FormulaLet A = (x1, y1) and B(x2, y2) be points in a coordinate plane. The distance between A and B is AB = (x2 - x1)2 + (y2 - y1)2 .

  7. Example :Let A = (-2,5) and B = (4,1). Find the midpoint, C, of AB. Then use the Distance Formula to verify that AC = CB. AC =  (1 – (-2))2 + (3 – 5)2 =  9 + 4 = 13 CB = (4 – 1)2 + (1 – 3)2 = 9 + 4 = 13

  8. Find the distance between the points whose coordinates are given: (6,4), (-8,11)(-5,8), (-10,14)(-4,-20), (-10,15)(5,-8), (0,0)

  9. Classwork :pg 74, 1 to 6 (SAW) Homework : pg 74, 15 to 22 pg 75, 23 to 28 pg 76, 40, 44 (SAW)

  10. Classwork : pg 77, 1 to 19 (SAW) Homework : RTN pgs 78 to 80

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