1 / 14

3.7 & 3.8 Constructing Points of Concurrency and Centroid

3.7 & 3.8 Constructing Points of Concurrency and Centroid. Objectives: I CAN discover points of concurrency of the angle bisectors, perpendicular bisectors, and altitudes of a triangle. I CAN explore the relationships between points of concurrency and inscribed and circumscribed circles.

rendor
Download Presentation

3.7 & 3.8 Constructing Points of Concurrency and Centroid

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. 3.7 & 3.8 Constructing Points of Concurrency and Centroid Objectives: I CAN discover points of concurrency of the angle bisectors, perpendicular bisectors, and altitudes of a triangle. I CAN explore the relationships between points of concurrency and inscribed and circumscribed circles. I CAN discover the concurrence of the medians of a triangle (the centroid) and its applications. I CAN explore length relationships among the segments into which the centroid divides each median. Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  2. Points of Concurrency What does Concurrent mean?

  3. Incenter Circumcenter Orthocenter Centroid Points of Concurrency Point of concurrency: The place where three or more lines meet. Make a checklist: (angle bisectors) (perpendicular bisectors) (altitudes) (medians) Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  4. Incenter ✔ Points of Concurrency (angle bisectors) Construct: Angle Bisector A B1 C C1 A1 B Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  5. Points of Concurrency ✔ Circumcenter (perpendicular bisectors) Construct: Perpendicular Bisector A b1 c1 C a1 B Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  6. Points of Concurrency Orthocenter (altitudes) ✔ Construct: Drop a perpendicular. A B1 C C1 A1 B Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  7. Points of Concurrency Centroid (median) ✔ Construct: Perpendicular Bisectors A B1 C1 C A1 B Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  8. Conjectures Angle Bisector Concurrency Conjecture The three angle bisectors of a triangle ____________________________. Perpendicular Bisector Concurrency Conjecture The three perpendicular bisectors of a triangle _______________. Altitude Concurrency Conjecture The three altitudes (or lines containing the altitudes) of a triangle ________________. meet at a point (are concurrent) are concurrent are concurrent Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  9. More Conjectures Circumcenter Conjecture The circumcenter of a triangle _______________________. Incenter Conjecture The incenter of a triangle __________________. Median Concurrency Conjecture The three medians of a triangle _____________. is equidistant from the vertices is equidistant from the sides are concurrent Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  10. Two More Conjectures Centroid Conjecture The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is ______ the distance from the centroid to the midpoint of the opposite side. Center of Gravity Conjecture The _______ of a triangle is the center of gravity of the triangular region. twice centroid Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  11. Construction 17-20: Lines in a Triangle Same distance from sides. Center of the circle inscribed in the triangle. Con 8: Incenter Angle Bisectors Same distance from vertices. Center of the circle circumscribed about the triangle. Con 9: Circumcenter Perpendicular Bisectors (Sides) Altitudes (heights) Con 10: Orthocenter 2/3 distance from vertex to midpoint of opposite side. Con 11: Centroid Medians Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  12. Vocabulary A) The point of concurrency for the three angle bisectors is the incenter. B) The point of concurrency for the three altitudes. C) The point of concurrency for the perpendicular bisector. D) The point of intersection E) Three or more line have a point in common. E ____ Concurrent ____ Point of Concurrency ____ Incenter ____ Circumcenter ____ Orthocenter D A C B Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  13. Vocabulary A) To draw (one figure) within another figure so that every vertex of the enclosed figure touches the outer figure. B) The balancing point for a polygon. C) To enclose a polygon within a configuration of lines, curves, or surfaces so that every vertex of the enclosed object is lying on the enclosing configuration. D) The point of concurrency of the three medians. ____ Circumscribed ____ Inscribed ____ Centroid ____ Center of Gravity C A D B Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

  14. Project Choose the project that you will do with your partner. The projects will be presented on: Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

More Related