Lesson 5.3 Lesson 5.3 Midsegment Theorem

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Presentation transcript:

Lesson 5.3 Lesson 5.3 Midsegment Theorem Honors Geometry Lesson 5.3 Midsegment Theorem

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

Midsegment The midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle

Lesson Investigation

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

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

Example 1 Illustrating the Midsegment Theorem Show that the midsegment MN is parallel to the side JK and half its length

Example 1 Solution Illustrating the Midsegment Theorem Begin by using the Midpoint Formula

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

Example 1 Solution Illustrating the Midsegment Theorem Now use the distance formula to find the lengths JK and MN (5,2) (2,1)

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?

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

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

Solution to Example 2 (3,5) (7,3) (1,1)

THE END