M is the midpoint of AB. Find AM and MB. Example 1 Find Segment Lengths M is the midpoint of AB. Find AM and MB. SOLUTION AM = MB = 2 1.

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M is the midpoint of AB. Find AM and MB. Example 1 Find Segment Lengths M is the midpoint of AB. Find AM and MB. SOLUTION AM = MB = 2 1 · AB = · 26 13 ANSWER AM = 13 and MB = 13. 8

P is the midpoint of RS. Find PS and RS. Example 2 Find Segment Lengths P is the midpoint of RS. Find PS and RS. SOLUTION P is the midpoint of RS, so PS = RP. Therefore, PS = 7. RS = = = 14 2 · RP 2 · 7 ANSWER PS = 7 and RS = 14. 9

Checkpoint Find Segment Lengths Find DE and EF. 1. Find NP and MP. 2.

Checkpoint 1. Find DE and EF. ANSWER DE = 9; EF = 9 2. Find NP and MP. Find Segment Lengths Find DE and EF. 1. ANSWER DE = 9; EF = 9 Find NP and MP. 2. ANSWER NP = 11; MP = 22

Line l is a segment bisector of AB. Find the value of x. Example 3 Use Algebra with Segment Lengths Line l is a segment bisector of AB. Find the value of x. SOLUTION AM = MB 5x = 35 5 5x = 35 x = 7 Check your solution by substituting 7 for x. 5x = 5(7) = 35 CHECK 12

Find the coordinates of the midpoint of AB. Example 4 Use the Midpoint Formula Find the coordinates of the midpoint of AB. A(1, 2), B(7, 4) a. A(–2, 3), B(5, –1) b. SOLUTION First make a sketch. Then use the Midpoint Formula. a. Let (x1, y1) = (1, 2) and (x2, y2) = (7, 4). M = 2 x1 + x2 , y1 + y2 = 2 1 + 7 , 2 + 4 = (4, 3) 16

Let (x1, y1) = (–2, 3) and (x2, y2) = (5, –1). M = 2 x1 + x2 , y1 + y2 Example 4 Use the Midpoint Formula b. Let (x1, y1) = (–2, 3) and (x2, y2) = (5, –1). M = 2 x1 + x2 , y1 + y2 = 2 –2 + 5 , 3 +(– 1) 2 3 , 1 = 17

Sketch PQ. Then find the coordinates of its midpoint. Checkpoint Use the Midpoint Formula Sketch PQ. Then find the coordinates of its midpoint. P(2, 5), Q(4, 3) 3. P(0, –2), Q(4, 0) 4. P(–1, 2), Q(–4, 1) 5.

Sketch PQ. Then find the coordinates of its midpoint. Checkpoint Use the Midpoint Formula Sketch PQ. Then find the coordinates of its midpoint. P(2, 5), Q(4, 3) 3. ANSWER (3, 4) P(0, –2), Q(4, 0) 4. ANSWER (2, –1) ANSWER – , 2 5 3 P(–1, 2), Q(–4, 1) 5.

Review

Use the figure at the right. 1. Use a protractor to approximate the measure of ABC. ANSWER 30° 2. Use your answer to Exercise 1 and the Angle Addition Postulate to find the measure of ABD. ANSWER 90° 3. Classify each of the three angles shown in the figure as acute, right, obtuse, or straight. ANSWER ABC is acute, CBD is acute, and ABD is right.

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