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5.1 and 5.2: Midsegments of Triangles Perpendicular and Angle bisectors

5.1 and 5.2: Midsegments of Triangles Perpendicular and Angle bisectors. Objectives : Students will be able to… Use properties of midsegments to solve problems Use properties of perpendicular and angle bisectors to find missing measurements. Midsegment of a Triangle.

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5.1 and 5.2: Midsegments of Triangles Perpendicular and Angle bisectors

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  1. 5.1 and 5.2: Midsegmentsof TrianglesPerpendicular and Angle bisectors Objectives: Students will be able to… Use properties of midsegments to solve problems Use properties of perpendicular and angle bisectors to find missing measurements

  2. Midsegment of a Triangle • Segment connecting the midpoints of 2 sides of a triangle B D E C A D is the midpoint of E is the midpoint of is the midsegment of

  3. Triangle MidsegmentTheorem If a segment joins the midpoints of 2 sides of a triangle, the segment is parallel to the 3rd side, and is ½ its length • Do NOT assume it’s a midsegment unless they tell you or you prove it.

  4. Triangle Midsegment Theorem is the midsegment of Therefore…. AND

  5. EXAMPLES: Find the value of the variables. 1. 2. A B C x x+2 E D 18 20

  6. Find the perimeter of D 5 3 E 7 A

  7. Find the value of the variable. (6x)° 30°

  8. In ∆XYZ, M, N, and P are midpoints. The perimeter of the ∆ MNP is 60 yd. Find NP and YZ. X 22 M P 24 Y Z N NAME ALL PARALLEL SEGMENTS:

  9. What is the measure of angle ANM? Angle A? Explain. A N M 65° C B

  10. Warm Up • What is a perpendicular bisector of a segment? • What is an angle bisector? • What does equidistant mean?

  11. is the perpendicular bisector of What do we know?

  12. Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

  13. Converse of Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. IS THE PERPENDICULAR BISECTOR OF SEGMENT AB 6 6

  14. EXAMPLES • Find PB and AQ. 14 7

  15. Find AD, x, and BC. 12 C D A 2x+6 3x+1 B

  16. What do we know about P? 10 10

  17. Definition The distance from a point to a line is defined as the length of the perpendicular segment from the point to the line.

  18. Angle Bisector Theorem • If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. 4 4

  19. Converse of Angle Bisector Theorem • If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

  20. You are designing a park, and you are in charge of building a walkway where every point on the walkway will be equidistant from 2 major monuments in the park. How would you figure out where to put the walkway?

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