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Angles and Segments Sections 1.4-1.6

Angles and Segments Sections 1.4-1.6. Students will be able to… Identify the bisector of an angle and determine if 2 adjacent angles are congruent Define and identify a perpendicular bisector Identify the midpoint of a segment Determine if 2 segments are congruent

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Angles and Segments Sections 1.4-1.6

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  1. Angles and SegmentsSections 1.4-1.6 Students will be able to… Identify the bisector of an angle and determine if 2 adjacent angles are congruent Define and identify a perpendicular bisector Identify the midpoint of a segment Determine if 2 segments are congruent Find the length of segments using the distance formula

  2. 2 segments with the same length are:CONGRUENT SEGMENTS ( ) AB = CD DON’T SAY Equal signs only compare numbers, never geometric figures C D A B 2 cm 2 cm

  3. Find the length of each segment. A B C D E AB= BC= CE= CD= WHICH TWO SEGMENTS ARE ?

  4. Midpoint: divides a segment into 2 congruent segments A midpoint, or any line, ray, or other segment through a midpoint, is said to BISECT the segment. (divides into 2 = parts) B is the midpoint; B A C

  5. You can use the definition of a midpoint to find lengths. C is the midpoint of AC = 2x +1 CB = 3x -4 Since we know by definition that AC = CB, set the expressions = to each other and solve for x.

  6. Find x, RM and MT. M T R 8x-36 5x+9

  7. Perpendicular Lines Two lines that intersect to form right angles The symbol means “is perpendicular to”

  8. Perpendicular Bisector Segment, line or ray to the segment at its midpoint It bisects the segment into 2 congruent segments

  9. Congruent Angles • Angles can be marked to show they are congruent using arcs at the vertex • Congruent angles will have the same number of arcs

  10. Angle Bisector J K bisects Therefore, N L A ray that divides an angle into two congruent, coplanar angles Its endpoint is at the angle’s vertex

  11. EXAMPLE: bisects Find the

  12. The Distance Formula • Used to find the distance between 2 points (or the length of segment between the 2 points): A( x1, y1) and B(x2, y2) You also could just plot the points and use the Pythagorean Theorem!!

  13. Find the distance between the two points. Round your answer to the nearest tenth. • T(5, 2) and R(-4, -1)

  14. Graph the 2 points on the coordinate plane. Then find the length of segment AB. A( -2, -3) and B(1, 3)

  15. Why are these pairs of points different?? • (2, 5) and (2, 9) • (-4, 7) and ( 3, 7)

  16. Midpoint Formula • Find the midpoint coordinates between 2 points • Find by averaging the x-coordinates and the y-coordinates of the endpoints (x2, y2) (x1, y1)

  17. Use the following segment to answer the questions: What is the length of the segment? What are the coordinates of the midpoint?

  18. Is R the midpoint of QT? Justify your answer.

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