1 / 25

Chapter 5.2 and 5.3

Chapter 5.2 and 5.3. Medians and Altitudes of Triangles And Inequalities in One Triangle. Definitions. Median of a Triangle – a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side. Centroid – The point of concurrency of the medians of a triangle.

myles-scott
Download Presentation

Chapter 5.2 and 5.3

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. Chapter 5.2 and 5.3 Medians and Altitudes of Triangles And Inequalities in One Triangle

  2. Definitions • Median of a Triangle – a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side. • Centroid – The point of concurrency of the medians of a triangle.

  3. Concept

  4. Use the Centroid Theorem In ΔXYZ, P is the centroid and YV = 12. Find YP and PV. Centroid Theorem YV = 12 Simplify.

  5. In ΔLNP, R is the centroid and LO = 30. Find LR and RO. A.LR = 15; RO = 15 B.LR = 20; RO = 10 C.LR = 17; RO = 13 D.LR = 18; RO = 12

  6. Use the Centroid Theorem In ΔABC, CG = 4. Find GE.

  7. In ΔJLN, JP = 16. Find PM. A. 4 B. 6 C. 16 D. 8

  8. Example 3 Find the Centroid on a Coordinate Plane SCULPTURE Lee is designing a sculpture that balances a triangle on top of a pole. In the artist’s design on the coordinate plane, the vertices are located at (1, 4), (3, 0), and (3, 8). What are the coordinates of the point where the artist should place the pole under the triangle so that it will balance? Understand You need to find the centroid of the triangle. This is the point at which the triangle will balance.

  9. Example 3 Find the Centroid on a Coordinate Plane

  10. The centroid P is the distance. So,the centroid is (2) or units to the right of A. The coordinates are . Example 3 Find the Centroid on a Coordinate Plane P

  11. Definition • Altitude of a triangle - segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. (aka height)

  12. Concept

  13. Concept

  14. Concept

  15. Concept

  16. Concept

  17. Use the Exterior Angle Inequality Theorem

  18. Use the Exterior Angle Inequality Theorem

  19. A. B. C. D.

  20. A. B. C. D.

  21. Concept

  22. Order Triangle Angle Measures List the angles of ΔABC in order from smallest to largest. Answer:C, A, B

  23. List the angles of ΔTVX in order from smallest to largest. A. X, T, V B. X, V, T C. V, T, X D. T, V, X

  24. Answer:AC, AB, BC Order Triangle Side Lengths List the sides of ΔABC in order from shortest to longest.

  25. A.RS, RT, ST B.RT, RS, ST C.ST, RS, RT D.RS, ST, RT List the sides of ΔRST in order from shortest to longest.

More Related