proportional segments between parallel lines. parallel lines and transversal alternate interior...

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Proportional Segments between Parallel Lines

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Page 1: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

Proportional Segments between Parallel Lines

Page 2: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

Parallel Lines and TransversalAlternate interior angles are congruent if the lines are parallelCorresponding angles are congruent if the lines are parallelGiven the picture list all corresponding angles, list all Alternate interior angles (assume lines are parallel)

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Page 3: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

Parallel/Proportionality Conjecture

If a line parallel to one side of a triangle passes through the other two sides, then it divides the other two sides proportionally. (This ratio is not the scale factor between the triangles)Conversely, if a line cuts two sides of a triangle proportionally, then it is parallel to the third side.

d

c

b

a

Assume line is parallel to base of triangle

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c

b

a

Page 4: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

Example

Page 5: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

Example

Page 6: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

Extended Parallel/ProportionalityConjecture

If two or more lines pass through two sides of a triangle parallel to the third side, then they divided the two sides proportionally.

f

e

d

c

b

a

f

d

c

ae

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Page 7: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

ExampleShow that sides are divided proportionally, set up similar triangles and just proportional sides.

Page 8: Proportional Segments between Parallel Lines. Parallel Lines and Transversal Alternate interior angles are congruent if the lines are parallel Corresponding

Homework

Pg 605 1-11 oddPg 627 1-9 odd