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Parallel Lines and Proportional PartsPowerPoint Presentation

Parallel Lines and Proportional Parts

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Parallel Lines and Proportional Parts

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Parallel Lines and Proportional Parts

Section 7.4

- Non parallel transversals that intersect parallel lines can be extended to form similar triangles.
- So, the sides of the triangles are proportional.

- If a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally.
- If BE || CD, then

- Find EC
- by ?
- EC = 6

- Find YX.
- YX = 3.2

- If a line intersects the other two sides and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side.
- If
- then BE || CD

- In triangle DEF, DH = 18, and HE = 36, and DG = ½ GF.
- To show GH || FE,
- Show
- Let GF = x, then DG = ½ x.

- Substitute
- Simplify
- Simplify

- Since the sides are proportional, then GH || FE.

- A midsegment of a triangle is parallel to one side of the triangle, and its length is one-half the length of that side.
- If D and E are mid-
- Points of AB and AC,
- Then DE || BC and
- DE = ½ BC

- Triangle ABC has vertices A(-2,2), B(2, 4) and C(4,-4). DE is the midsegment of triangle ABC.
- Find the coordinates of D and E.
- D midpt of AB
- D(0,3)

- E midpt of AC
- E(1, -1)
- Part 2 - Verify BC || DE
- Do this by finding slopes
- Slope of BC = -4 and slope of DE = -4
- BC || DE

- Part 3 – Verify DE = ½ BC
- To do this use the distance formula
- BC = which simplifies to
- DE =
- DE = ½ BC

- 1. If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.

- If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

- 1. In the figure, Larch, Maple, and Nutthatch Streets are all parallel. The figure shows the distance between city blocks. Find x.

- Find x and y.
- Given: AB = BC
- 3x + 4 = 6 – 2x
- X = 2
- Use the 2nd corollary to say DE = EF
- 3y = 5/3 y + 1
- Y = ¾