Thinking Page… Directions: Take out your math encyclopedia and review your notes for this unit. Write two paragraphs using complete sentences and correct.

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Presentation transcript:

Thinking Page… Directions: Take out your math encyclopedia and review your notes for this unit. Write two paragraphs using complete sentences and correct grammar to reflect on the following writing prompts. Reflection #1: What is the most significant thing you learned this week? Reflection #2: What questions are still unanswered at the end of this week?

5.3 Concurrent Lines, Medians, and Altitudes Stand 0_ Can you figure out the puzzle below??? No one understands!

Learning Target… To identify properties of perpendicular bisectors and angle bisectors, medians, and altitudes. Purpose: To be able to find locations in a park to place a fountain, statue, playground, etc....

Definitions Concurrent Lines: Three or more lines that meet at one point. Point of Concurrency: The point at which concurrent lines meet. l m n P k

Properties of Bisectors Theorem 5-6: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. Circumcenter of the Triangle: The point of concurrency of the perpendicular bisectors of a triangle.

Properties of Bisectors Theorem 5-7: The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. Incenter of the Triangle: The point of concurrency of the angle bisectors of a triangle.

Definitions Altitude of a Triangle: Perpendicular segment from a vertex to the line containing the opposite side. Median of a Triangle: A segments whose endpoints are a vertex and the midpoint of the opposite side.

Properties of Medians Centroid of a Triangle: The point of concurrency of the medians of a triangle. Theorem 5-8: The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite sides.

Properties of Medians In the figure below, DE = 6 and AD = 16. Find DB and AF. F

Properties of Altitudes Orthocenter of a Triangle: The point of concurrency of the lines containing the altitudes of a triangle. Theorem 5-9: The lines that contain the altitudes of a triangle are concurrent.

Sum It Up Figureconcurrent at.. which is… bisector circumcenter incenter centroid orthocenter median bisector altitude equidistant from vertices equidistant from sides 2/3 distance from vertices to midpoint

5.3 Concurrent Lines, Medians, and Altitudes HW 5.3: #8-9, 11-16, 19-22, 28 KNEE LIGHT Can you figure out the puzzle below??? Neon Lights