1 / 25

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.

joyce
Download Presentation

Find each measure of MN . Justify

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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).

More Related