5.1: Midsegments of Triangles

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Presentation transcript:

5.1: Midsegments of Triangles Objectives: To use properties of midsegments to solve problems

Warm-Up Find the distance between the 2 points A(-1,-4) and B(2, 3). Find the coordinates of the midpoint of the segment with endpoints A(-2, 3) and B(4, 1)

Midsegment of a Triangle Segment connecting the midpoints of 2 sides of a triangle B D E C A D is the midpoint of E is the midpoint of is the midsegment of

Triangle Midsegment Theorem If a segment joins the midpoints of 2 sides of a triangle, the segment is parallel to the 3rd side, and is ½ its length Do NOT assume it’s a midsegment unless they tell you or you prove it.

Triangle Midsegment Theorem is the midsegment of Therefore…. AND

EXAMPLES: Find the value of the variables. 1. 2. A B C x x+2 E D 18 20

Find the perimeter of D 5 3 E 7 A

Find the value of the variable. (6x)° 30°

In ∆XYZ, M, N, and P are midpoints. The perimeter of the ∆ MNP is 60 yd. Find NP and YZ. 22 M P 24 Y Z N NAME ALL PARALLEL SEGMENTS:

What is the measure of angle ANM? Angle A? Explain. 65° C B