Unit 3 Homework 3 Proving Lines Parallel Answer Key (2024)

FAQs

How do you prove lines are parallel answers? ›

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.

Theorem 12: Three parallel lines theorem

If three parallel lines are cut by two transversals, then the segments formed on the transversal have equal proportion. Proof: Here lines p, q, and r are parallel to each other. And these lines are cut by two transversal t and s at points A, B, C, and D, E, and F respectively.

To be parallel, two lines must have the same gradient. The gradient of y = 3 x + 7 is 3. Any line with a gradient of 3 will be parallel to y = 3 x + 7 . Two examples are y = 3 x − 2 and y = 3 x + 11.6 .

The three parallel line theorem (arbitrary name) states that: If three or more parallel lines are cut by two transversals, then they divide the transversals proportionally. For example, if x, y, and z are parallel, then ABDE=BCEF.

Consider a line l, and suppose that we draw two more lines m and n such that l ∥ m and l ∥ n. This proves that m must be parallel to n. We formalize this result in the form of a theorem. Theorem: Two or more lines which are parallel to the same line will be parallel to each other.

The basic proportionality theorem (Thales's theorem) states that if three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.

If two parallel lines are cut by a transversal, then corresponding angles are congruent. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Theorem 1.4.

If two lines are parallel then the interior angles on the same side of the transversal are supplementary (they add uP to 180∘). If the interior angles of two lines on the same side of the transversal are supplementary then the lines must be parallel.

Parallel, means running along each other. It is used mostly for straight lines, but two curved lines can also be 'parallel', like for example the rails of the railway. Congruent means equal in both shape and size.

What are 4 examples of parallel lines? ›

Parallel line examples in real life are railroad tracks, the edges of sidewalks, markings on the streets, zebra crossing on the roads, the surface of pineapple and strawberry fruit, staircase and railings, etc.

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

It's easy to eyeball parallel lines, but you'll want to know a way to prove it. To determine that two lines are parallel, you need to demonstrate that they have the same slope and never intersect, no matter how far they are extended in both directions.