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 the length of XY. 3. Find.

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Presentation transcript:

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 the length of XY. 3. Find the length of AB. 4. Find the slope of AB. 5. Find the slope of XY. (3, 5), (8, 5) 5 10

5.1 Midsegment of triangle Theorem Target: SWBAT use properties of triangle midsegments.

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 relationship shown is true for the three midsegments of every triangle.

Example 2A: Using the Triangle Midsegment Theorem Find each measure. BD ∆ Midsegment Thm. Substitute 17 for AE. BD = 8.5 Simplify.

Example 2B: Using the Triangle Midsegment Theorem Find each measure. mCBD ∆ Midsegment Thm. mCBD = mBDF Alt. Int. s Thm. mCBD = 26° Substitute 26° for mBDF.

Check It Out! Example 2a Find each measure. JL ∆ Midsegment Thm. Substitute 36 for PN and multiply both sides by 2. 2(36) = JL 72 = JL Simplify.

Check It Out! Example 2b Find each measure. PM ∆ Midsegment Thm. Substitute 97 for LK. PM = 48.5 Simplify.

Check It Out! Example 2c Find each measure. mMLK ∆ Midsegment Thm. mMLK = mJMP Similar triangles mMLK = 102° Substitute.

Lesson Quiz: Part I Use the diagram for Items 1–3. Find each measure. 1. ED 2. AB 3. mBFE 10 14 44°

Lesson Quiz: Part II 4. Find the value of n. 5. ∆XYZ is the midsegment triangle of ∆WUV. What is the perimeter of ∆XYZ? 16 11.5