Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

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Presentation transcript:

Section 4.7 Medians, Altitudes, and Perpendicular Bisectors WARM UP

Measure each side of the triangle. Activity Part 1 Draw a triangle. Label it ∆BOY. Measure each side of the triangle. Find and mark the MIDPOINT of each side.

Activity Part 2 Draw a line connecting Point B to the MIDPOINT on the OPPOSITE SIDE. Draw a line connecting Point O to the MIDPOINT on the OPPOSITE SIDE. Draw a line connecting Point Y to the MIDPOINT on the OPPOSITE SIDE.

What is a Median? A segment from a vertex to the midpoint of the opposite side. Always three medians. See the medians for a given triangle.

What is a Centroid? x = 6 y = 5.5 x y 3 11 Centroid: the point where all three medians meet The medians of a triangle divide one another into ratios of 2:1. x = 6 x y 3 11 y = 5.5

Activity 2 Draw a triangle. Label it ∆ WIG. Draw a segment from W to the opposite side so that it makes a right angle with that side.

What is an Altitude? The perpendicular segment from a vertex to the opposite side. Altitudes can be drawn OUTSIDE of the triangle.

Orthocenter: point where three altitudes meet

Which line is the median? Which line is the altitude? a b

What are Perpendicular Bisectors? A line or ray that is perpendicular to the segment at its midpoint. Does NOT have to start at a VERTEX

Perpendicular Bisectors What is true of AB and AC?

Circumcenter: point where three perpendicular bisectors meet.

TOGETHER, OPEN YOUR TEXTBOOK Page 155 - Classroom Exercises #1-6

Partner Practice Page 157 # 19 (a, b, and c) TO BE HANDED IN! Make it neat. I only need one per group.