Midsegments of Triangles

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Presentation transcript:

Midsegments of Triangles

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.

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.

Example 3: Indirect Measurement Application 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? ∆ Midsegment Thm. Substitute 46 for PQ. ST = 23 Simplify. The length of the support ST is 23 inches.

Check It Out! Example 3 What if…? Suppose Anna’s result in Example 3 (p. 323) is correct. To check it, she measures a second triangle. How many meters will she measure between H and F? ∆ Midsegment Thm. Substitute 1550 for AE. HF = 775 m Simplify.

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

Identifying Parallel Segments What are the three pairs of parallel segments in DEF?

Finding Lengths In QRS, T, U, and B are midpoints. What are the lengths of TU, UB, and QR?

In the figure below, AD = 6 and DE = 7. 5 In the figure below, AD = 6 and DE = 7.5. What are the lengths of DC, AC, EF, and AB?

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?