5-4 The Triangle Midsegment Theorem Section 5.4 Holt McDougal Geometry

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Presentation transcript:

5-4 The Triangle Midsegment Theorem Section 5.4 Holt McDougal Geometry Holt Geometry

Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 1–5. 1. Find X and Y, the midpoints of AC and CB. 2. Find XY. 3. Find AB. 4. Find the slope of AB. 5. Find the slope of XY. 6. What is the slope of a line parallel to 3x + 2y = 12?

A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.

The vertices of ∆XYZ are X(–1, 8), Y(9, 2), and Z(3, –4) The vertices of ∆XYZ are X(–1, 8), Y(9, 2), and Z(3, –4). M and N are the midpoints of XZ and YZ. Show that and .

The relationship shown in Example 1 is true for the three midsegments of every triangle.

Find each measure. BD 2. mCBD

Find each measure. 1. JL 2. PM 3. mMLK

In an A-frame support, the distance PQ is 46 inches In an A-frame support, the distance PQ is 46 inches. What is the length of the support ST if S and T are at the midpoints of the sides?

Lesson Quiz: Part I Find each measure. 1. ED 2. AB 3. mBFE

Lesson Quiz: Part II 4. Find the value of n. 5. ∆XYZ is the midsegment triangle of ∆WUV. What is the perimeter of ∆XYZ?