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Triangle Proportionality Theorem Examples with Midpoints

Explore examples of using the Triangle Proportionality Theorem to find midpoints of triangles. Calculate coordinates of midpoints using formulas and verify with given data.

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Triangle Proportionality Theorem Examples with Midpoints

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  1. In and Find SU. S From the Triangle Proportionality Theorem, Example 4-1a

  2. In and Find BY. B Example 4-1c Answer: 15.75

  3. Triangle ABC has vertices A(–2, 2), B(2, 4,) and C(4, –4). is a midsegment of Find the coordinates ofD and E. Use the Midpoint Formula to find the midpoints of (2, 4) (-2, 2) (4, –4) Example 4-3a Answer: D(0, 3), E(1, –1)

  4. Triangle ABC has vertices A(–2, 2), B(2, 4) and C(4, –4). is a midsegment of Verify that If the slopes of slope of (2, 4) slope of (-2, 2) Answer: Because the slopes of (4, –4) Example 4-3c

  5. Triangle ABC has vertices A(–2, 2), B(2, 4) and C(4, –4). is a midsegment of Verify that (2, 4) (-2, 2) Answer: (4, –4) Example 4-3e First, use the Distance Formula to find BC and DE.

  6. 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 Answer: Since the slope of and the slope of Answer: Therefore, Example 4-3h Answer: W(0, 2), Z(1, –3)

  7. Example 4-4a In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem. Answer: 32

  8. Example 4-4c In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. Answer: 5

  9. Example 4-5a Find x and y. To find x: Answer: x = 6; y = 3

  10. Example 4-5d Find a and b. Answer: a = 11; b = 1.5

  11. HW: Page 312

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