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 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.TRANSCRIPT
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?
Holt McDougal Geometry
5-4 The Triangle Midsegment Theorem
Prove and use properties of triangle midsegments.
Objective
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.
Holt McDougal Geometry
5-4 The Triangle Midsegment Theorem
The relationship shown in Example 1 is true for the three midsegments of every triangle.
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
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°
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.
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.
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
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.
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.
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.
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.
Holt McDougal Geometry
5-4 The Triangle Midsegment Theorem
Assignment• Pg. 336 (11-26)