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Lesson 5.3 Lesson 5.3 Midsegment Theorem
Honors Geometry Lesson 5.3 Midsegment Theorem
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What You Should Learn Why You Should Learn It
Goal 1: How to identify and construct the midsegments of a triangle Goal 2: How to use properties of midsegments to solve real-life problems You can use the midsegments of a triangle to answer questions about triangles that occur in real-life situations such as building a roof framework
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Midsegment The midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle
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Lesson Investigation
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Observations about midsegments
Midsegment is half the length of the side it is parallel to Midsegment is parallel to the third side of the triangle
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Theorem 5.6 Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length
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Example 1 Illustrating the Midsegment Theorem
Show that the midsegment MN is parallel to the side JK and half its length
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Example 1 Solution Illustrating the Midsegment Theorem
Begin by using the Midpoint Formula
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Example 1 Solution Illustrating the Midsegment Theorem
Now find the slopes of JK and MN (5,2) (2,1) Because JK and MN have the same slope, they must be parallel
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Example 1 Solution Illustrating the Midsegment Theorem
Now use the distance formula to find the lengths JK and MN (5,2) (2,1)
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Using the Midsegment Theorem to draw a triangle
Suppose you are given the three midpoints of the sides of a triangle. Using only these three points, is it possible to construct the original triangle?
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Example 2 Using Midpoints to draw a triangle
The midpoints of the sides of a triangle are L(4,2), M(2,3) and N(5,4). What are the coordinates of the vertices of the triangle? Hint: find the slopes of each midsegment
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Example 2 Using Midpoints to draw a triangle
The midpoints of the sides of a triangle are L(4,2), M(2,3) and N(5,4). What are the coordinates of the vertices of the triangle? Example 2 Using Midpoints to draw a triangle Draw a line through M that has a slope of 2 Draw a line through L that has a slope of ⅓ Draw a line through N that has a slope of -½
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Solution to Example 2 (3,5) (7,3) (1,1)
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THE END
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