holt mcdougal geometry 5-4 the triangle midsegment theorem warm up use the points a(2, 2), b(12, 2)...

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Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem 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?

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Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem 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.

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Page 1: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment Theorem

Warm UpUse 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?

Page 2: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment Theorem

Prove and use properties of triangle midsegments.

Objective

Page 3: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment Theorem

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.

Page 4: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment Theorem

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

Page 5: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment TheoremExample 2A: Using the Triangle Midsegment Theorem

Find each measure.

BD = 8.5

∆ Midsegment Thm.

Substitute 17 for AE.

Simplify.

BD

Page 6: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment TheoremExample 2B: Using the Triangle Midsegment Theorem

Find each measure.

mCBD

∆ Midsegment Thm.Alt. Int. s Thm.

Substitute 26° for mBDF.

mCBD = mBDF mCBD = 26°

Page 7: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment TheoremThe positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

Page 8: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment TheoremExample 2A: Ordering Triangle Side Lengths and Angle

Measures Write the angles in order from smallest to largest.

The angles from smallest to largest are F, H and G.

The shortest side is , so the smallest angle is F.

The longest side is , so the largest angle is G.

Page 9: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment TheoremExample 2B: Ordering Triangle Side Lengths and Angle

Measures Write the sides in order from shortest to longest.mR = 180° – (60° + 72°) = 48° The smallest angle is R, so the shortest side is .The largest angle is Q, so the longest side is .

The sides from shortest to longest are

Page 10: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment Theorem

A triangle is formed by three segments, but not every set of three segments can form a triangle.

Page 11: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment Theorem

A certain relationship must exist among the lengths of three segments in order for them to form a triangle.

Page 12: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment TheoremExample 3A: Applying the Triangle Inequality Theorem

Tell whether a triangle can have sides with the given lengths. Explain.

7, 10, 19

No—by the Triangle Inequality Theorem, a triangle cannot have these side lengths.

Page 13: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment TheoremExample 4: Finding Side Lengths

The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the third side.

Page 14: Holt McDougal Geometry 5-4 The Triangle Midsegment Theorem Warm Up Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 15. 1. Find X and Y, the

Holt McDougal Geometry

5-4 The Triangle Midsegment Theorem

Assignment• Pg. 336 (11-26)

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