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Lesson 4 Contents Example 1Find the Length of a Side Example 2Determine Parallel Lines Example 3Midsegment of a Triangle Example 4Proportional Segments Example 5Congruent Segments
Example 4-1a From the Triangle Proportionality Theorem, In and Find SU. S
Example 4-1b Substitute the known measures. Cross products Multiply. Divide each side by 8. Simplify. Answer:
Example 4-1c Answer: In and Find BY. B
Example 4-2a In and Determine whether Explain.
Example 4-2b In order to show that we must show that Since the sides have proportional length. Answer: since the segments have proportional lengths,
Example 4-2c In and AZ = 32. Determine whether Explain. Answer: No; the segments are not in proportion since X
Example 4-3a Triangle ABC has vertices A(–2, 2), B(2, 4,) and C(4, –4). is a midsegment of Find the coordinates of D and E. (-2, 2) (2, 4) (4, –4)
Example 4-3b Use the Midpoint Formula to find the midpoints of Answer: D(0, 3), E(1, –1)
Example 4-3c Triangle ABC has vertices A(–2, 2), B(2, 4) and C(4, –4). is a midsegment of Verify that (-2, 2) (2, 4) (4, –4)
Example 4-3d slope of If the slopes of slope of Answer: Because the slopes of
Example 4-3e Triangle ABC has vertices A(–2, 2), B(2, 4) and C(4, –4). is a midsegment of Verify that (-2, 2) (2, 4) (4, –4)
Example 4-3f First, use the Distance Formula to find BC and DE.
Example 4-3g Answer:
Example 4-3h Triangle UXY has vertices U(–3, 1), X(3, 3), and Y(5, –7). is a midsegment of
a. Find the coordinates of W and Z. b. Verify that c. Verify that Example 4-3i Answer: W(0, 2), Z(1, –3) Answer: Since the slope of and the slope of Answer: Therefore,
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