2-4: Slopes of Parallel and Perpendicular Lines

Lesson 2-4: Slopes of Parallel and Perpendicular Lines

Standards:
G.RL.1.1: Use undefined terms, definitions, postulates, and theorems in logical arguments/proofs.

G.RL.1.2: Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive.

G.2D.1.1: Use properties of parallel lines cut by a transversal to determine angle relationships and solve problems.

G.2D.1.2: Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs.

G.2D.1.4: Apply theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs.

G.2D.1.6: Use coordinate geometry and algebraic reasoning to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.

G.2D.1.7: Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures).

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Model & Discuss

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Try It! #1: A fourth level of scaffolding is 6 feet above the third level. Is the fourth flight of stairs parallel to any of the other flights? Explain.

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Try It! #2:

​Are lines m and q parallel?

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Try It! #3

​a. Are lines h and ℓ perpendicular?

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Try It! #3

b. Are lines k and m perpendicular?

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Try It! #4

​What are equations of lines parallel and perpendicular to the given line k passing through point T?

a. y=-3x + 2; T(3,1)

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Try It! #4

​What are equations of lines parallel and perpendicular to the given line k passing through point T?

b. $$y=\frac{3}{4}x-5$$ ; T(12, -2)

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Try It! #5

​The architect wants the front of the shed to be parallel to the back of the house. If one corner of the shed is at (0, 5), can the other corner be at (3, 6.5)? Explain.