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Find each measure of MN . Justify

Find each measure of MN . Justify. MN = 2.6 Perpendicular Bisector Theorem. Write an equation to solve for a. Justify. 3 a + 20 = 2 a + 26 Converse of  Bisector Theorem . Find the measures of BD and BC . Justify. BD = 12 BC =24 Converse of  Bisector Theorem.

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Find each measure of MN . Justify

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  1. Find each measure of MN. Justify MN = 2.6 Perpendicular Bisector Theorem

  2. Write an equation to solve for a. Justify 3a + 20 = 2a + 26 Converse of  Bisector Theorem

  3. Find the measures of BD and BC. Justify BD = 12 BC =24 Converse of  Bisector Theorem

  4. Find the measure of BC. Justify BC = 7.2  Bisector Theorem

  5. Write the equation to solve for x. Justify your equation. 3x + 9 = 7x – 17  Bisector Theorem

  6. Find the measure. mEFH, given that mEFG = 50°. Justify m EFH = 25 Converse of the  Bisector Theorem

  7. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints C(6, –5) and D(10, 1).

  8. Perpendicular Bisectors of a triangle… • bisect each side at a right angle • meet at a point called the circumcenter • The circumcenter is equidistant from the 3 vertices of the triangle. • The circumcenter is the center of the circle that is circumscribed about the triangle. • The circumcenter could be located inside, outside, or ON the triangle. C

  9. Paste-able! Angle Bisectors of a triangle… • bisect each angle • meet at the incenter • The incenter is equidistant from the 3 sides of the triangle. • The incenter is the center of the circle that is inscribed in the triangle. • The incenter is always inside the circle. I

  10. DG, EG, and FG are the perpendicular bisectors of ∆ABC. Find GC. GC = 13.4

  11. MZ and LZ are perpendicular bisectors of ∆GHJ. Find GM GM = 14.5

  12. Z is the circumcenter of ∆GHJ. GK and JZ GK = 18.6 JZ = 19.9

  13. Find the circumcenter of ∆HJK with vertices H(0, 0), J(10, 0), and K(0, 6).

  14. MP and LP are angle bisectors of ∆LMN. Find the distance from P to MN.

  15. MP and LP are angle bisectors of ∆LMN. Find mPMN. mPMN = 30

  16. 5-3: Medians and Altitudes B • Medians of triangles: • Endpoints are a vertex • and midpoint of opposite side. • Intersect at a point called the centroid • Its coordinates are the average of the 3 vertices. • The centroid is ⅔of the distance from each vertex to the midpoint of the opposite side. • The centroid is always located inside the triangle. X Y P  A C Z

  17. 5-3: Medians and Altitudes • Altitudes of a triangle: • A perpendicular segment from a vertex to the line containing the opposite side. • Intersect at a point called the orthocenter. • An altitude can be inside, outside, or on the triangle.

  18. In ∆LMN, RL = 21 and SQ =4. Find LS. LS = 14

  19. In ∆LMN, RL = 21 and SQ =4. Find NQ. 12 = NQ

  20. In ∆JKL, ZW = 7, and LX = 8.1. Find KW. KW = 21

  21. Example 2: Problem-Solving Application A sculptor is shaping a triangular piece of iron that will balance on the point of a cone. At what coordinates will the triangular region balance?

  22. Find the average of the x-coordinates and the average of the y-coordinates of the vertices of ∆PQR. Make a conjecture about the centroid of a triangle.

  23. X Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 1).

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