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Distance & Midpoints Angle Measure

Distance & Midpoints Angle Measure. Notes 2 – Sections 1.3 & 1.4. Essential Learnings. Students will understand and be able to find distance and the midpoint of a segment. Students will be able to construct, copy and bisect segments.

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Distance & Midpoints Angle Measure

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  1. Distance & MidpointsAngle Measure Notes 2 – Sections 1.3 & 1.4

  2. Essential Learnings • Students will understand and be able to find distance and the midpoint of a segment. • Students will be able to construct, copy and bisect segments. • Students will understand and be able to measure and classify angles. • Students will be able to identify and use congruent and special pairs of angles. • Students will be able to identify perpendicular lines.

  3. Vocabulary • The distance between two points is the length of the segment with those points as the endpoints. • Midpoint – the point halfway between the endpoints of a segment. x1 M x2

  4. Distance Formula • If P has the coordinates (x1,y1) and Q has coordinates (x2,y2) then:

  5. Example 1 • Find the distance between the pair of points. M(4,0) and L(-2,-3).

  6. Midpoint Formula • If has the endpoints P(x1,y1) and Q(x2,y2) in the coordinate plane, then the midpoint M of is:

  7. Example 2 • Find the coordinates of the midpoint of a segment with endpoints W(12,2) and X(7,9).

  8. Example 3 • Find the coordinates of the missing endpoint if B is the midpoint . A(1,7) and B (-3,1)

  9. Example 4 • Suppose M is the midpoint of . Use the given information to find the missing measure or value. FM = 5x+13, MG = 5-3x, FG = ?

  10. Constructions • Need compass! Construct segment Copy segment Bisect a segment

  11. Vocabulary • Ray – begins at a point and extends indefinitely in one direction. • Angle – formed by two rays that have a common end point. Q P PQ

  12. Vocabulary • Vertex – the common endpoint of an angle. • Side – one of the rays that make up an angle. • Opposite rays – rays that share a common endpoint and are collinear.

  13. Angles • Naming angles – use three letters with the vertex as the middle letter or can name the angle using the vertex but only if there is only one angle located at that vertex. J 2 L K

  14. Example 5 • Name all angles that have B as the vertex. E D B F A C G

  15. Example 6 • Write another name for each angle. ∠DCB ∠BAC ∠4 D B 2 5 1 3 4 A C E

  16. Measures of Angles • Angles are measured in degrees. Use your protractor to measure angles.

  17. Classifying Angles Acute angle Right angle Obtuse angle m∠A< 90⁰ m∠A= 90⁰ 90⁰<m∠A <180⁰ A A A

  18. Copying an Angle • Use your compass.

  19. Angle Bisector • Angle bisector – a ray that divides an angle into two congruent angles. C ∠ABC ≅ ∠CBD 70⁰ 70⁰ A D B

  20. Constructing Angle Bisector • Use your compass.

  21. Example 7 Ray QS bisects ∠PQT. m∠PQT=60⁰ andm∠PQS=4x+14, solve for x. T S P Q R

  22. Example 8 Ray KM bisects ∠NKL. m∠MKL=3x+13 andm∠NKM=6x-2, m∠NKL=? N M J K L

  23. Assignment Page 32: 19-29 odd, 41-53 odd Page 41-44: 20-25, 37-41 odd, 64, 65 Signed Slip Cover Textbook

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