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Section 5-1 and 5-2: Midsegments and Bisectors in Triangles

Section 5-1 and 5-2: Midsegments and Bisectors in Triangles. March 5, 2012. Warm-up. Warm-up: Get your folder on side table and Pick up hand-out on side table Complete “Investing Midsegments” handout: #1-16 (yes, you can write on it). Warm-up.

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Section 5-1 and 5-2: Midsegments and Bisectors in Triangles

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  1. Section 5-1 and 5-2: Midsegments and Bisectors in Triangles March 5, 2012

  2. Warm-up Warm-up: • Get your folder on side table and • Pick up hand-out on side table Complete “Investing Midsegments” handout: #1-16 (yes, you can write on it)

  3. Warm-up

  4. Section 5-1 and 5-2: Midsegments and Bisectors in Triangles • Objectives: Today you will learn to use properties of • midsegments • perpendicular bisectors, and • angle bisectors to solve problems.

  5. Section 5-1: Midsegments of Triangles A midsegment of a triangle is a segment connecting the midpoints of two sides. Triangle Midsegment Theorem: If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length. (p. 244) is the midsegment of ΔABC

  6. Section 5-1 Example 1: R is midpoint of and S is midpoint of If YZ = 10, then RS = ____ If RS = 7, then YZ = ____

  7. Section 5-1 Example 2: R is midpoint of and M is the midpoint of Find value of x.

  8. Section 5-1 Example 3: R is midpoint of and M is the midpoint of Find value of x

  9. Section 5-1 Example 4: Given congruent segments as marked, find value of x

  10. Section 5-1 Example 5: In ΔXYZ, M, N, and P are midpoints. The perimeter of ΔMNP is 60. Find NP, YZ and perimeter of ΔXYZ. NP = ______ YZ = ______ Perimeter of ΔXYZ = ______

  11. Section 5-1 Example 6: Given segments as marked, find x and y.

  12. Section 5-1 Example 7: Given segments as marked, find all missing angle measurements

  13. Section 5-2: Perpendicular Bisectors A perpendicular bisector is a line or segment that is perpendicular to a segment at its midpoint.

  14. Section 5-2: Perpendicular Bisectors (p. 249) Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then the point is equidistance from the endpoints of the segment. Converse of the Perpendicular Bisector Theorem: If a point is equidistance from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

  15. Section 5-2: Angle Bisectors Distance from a point to a line is the length of the perpendicular segment from the point to the line.

  16. Section 5-2: Angle Bisectors (p. 250) Angle Bisector Theorem: If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. Converse of the 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.

  17. Section 5-2: Example 1: Given segments and angles as marked AB = _____ CD = _____ Why?

  18. Section 5-2: Example 2: Given angles as marked x = ____ FB = ____ FD = ____ CD = ____ Perimeter of CDFB = _______ How do you know?

  19. Section 5-2: Real Life Example Baseball (and Softball!) Diamonds are created using Angle Bisectors

  20. Section 5-2: Example 3: Given segments and angles as marked x = _____ m∠GYE = ______ m∠GYO = ______ m∠RTY = ______ m∠YEG = ______

  21. Reteaching 5-2: Practice Workbook, p. 55

  22. Wrap-up • Today you learned to use properties of midsegments, perpendicular bisectors, and angle bisectors to solve problems. • Tomorrow you’ll learn about concurrent lines, medians and altitudes of a triangle • Homework • pp. 246-247, #1-10, 13, 20-26, 32 • pp. 251-253, #1-16, 46

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