1 / 15

5.3: Concurrent Lines, Medians and Altitudes

5.3: Concurrent Lines, Medians and Altitudes. Objectives : Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify properties of medians and altitudes of triangles. Vocabulary. Concurrent: 3 or more lines intersect at a point

netis
Download Presentation

5.3: Concurrent Lines, Medians and Altitudes

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. 5.3: Concurrent Lines, Medians and Altitudes Objectives: Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify properties of medians and altitudes of triangles

  2. Vocabulary Concurrent: 3 or more lines intersect at a point Point of Concurrency: where the lines intersect

  3. Median of a Triangle A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side

  4. Special Triangle Segments

  5. Additional Info about Circumcenters: • If you were to draw a circle around a triangle, where each vertex of the triangle are points on the circle, the circle would be circumscribed about that triangle • The circumcenter of the triangle is ALSO the center of the circle circumscribed about it

  6. Perpendicular Bisectors Acute triangle: Circumcenter inside triangle Right triangle: Circumcenter lies ON the triangle Obtuse Triangle: Circumcenter is outside triangle

  7. Find the center of the circle that you can circumscribe about the triangle with vertices (0, 0), (-8,0) and (0,6). • Plot the points on a coordinate plane. • Draw the triangle • Draw the perpendicular bisectors of at least 2 sides. • The circumcenter of this triangle will be the center of the circle.

  8. Incenters A circle is inscribed in a triangle when the circle is tangent to each side (also called an incircle) The incenter of a triangle is the center of an inscribed circle

  9. Additional Info about incenters: • The incenter of ALL types of triangles is always INSIDE the triangle.

  10. Example: Find the values of the variables. 4 y 10 x

  11. WHAT IS THE DIFFERENCE BETWEEN A MEDIAN AND A PERPENDICULAR BISECTOR??

  12. CENTROIDS G is the centroid AG = AD BG = BF CG= CE

  13. O is the centroid of triangle ABC. CE = 11 FO = 10 CO = 8 Find EB. Find OD. Find FB. Find CD. If AO = 6, find OE.

  14. Altitude of a Triangle The perpendicular segment from the vertex to the line containing the opposite side Obtuse Triangle: Outside Acute Triangle: Inside Right Triangle: Side

  15. What is the difference between an altitude and a perpendicular bisector?

More Related