Parallel Lines And Transversals Proofs

So when a transversal cuts through any set of parallel lines it forms sets of congruent angles and supplementary angles. then it is true that the lines are parallel. You will be proving these with two column proofs. See Example In a two column proof, a statement is made that work toward the final conclusion.

In the diagram shown on page 330, the two lines cut by the transversal are not parallel lines. However, when two lines are parallel, many statements may be postulated and proved about these angles. Theorem 9.1a Given and are cut by transversal at points E and F, respectively 1 2. Prove Proof To prove this theorem, we will use an indirect proof.

140 Chapter 3 Parallel and Perpendicular Lines Proving Theorems about Parallel Lines Proving the Alternate Interior Angles Converse Prove that if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. SOLUTION Given 4 5 Prove g h STATEMENTS REASONS 1. 4 1. 5 Given 2

3.2- Parallel Lines and Transversals Know which angles are congruent and supplementary 3.3 Proving Lines Parallel Converses used to show lines are PARALLEL If two lines are parallel, then they ALWAYS..SOMETIMES..NEVER intersect. 2. If one line is skew to another, then they are ALWAYS..SOMETIMES..NEVER coplanar.

Let and be the intersections of transversal with lines and , respectively.Let be the midpoint of . a Rotate about , which takes to itself, and which swaps and because distances are preserved. b Because and because a side of i.e., is mapped to a side of i.e., , it must be that the other side of which lies on is mapped to the other side of which lies on line .

when parallel lines are cut by a transversal. Activity Use your notebook paper and the lines on it to draw a pair of parallel lines. Then, using a ruler, draw a third line a transversal that intersects the parallel lines. Label the parallel lines as lines m and n. Label the transversal as t. Check for congruence!

Draw two parallel lines and a transversal on the whiteboard to illustrate the converse of the same-side interior angles postulate This is a simple activity that will help students reinforce their skills at proving lines are parallel. Introduce this activity after you've familiarized students with the converse of the theorems and

Proof of Theorem 3-1 If a transversal intersects two parallel lines, then alternate interior angles are congruent. Given a 6b Prove amp1 gt amp3 Statements Reasons 1. a 6b 1. When you see two parallel lines and a transversal, and you know the measure of one angle, you can nd the measures of all the angles.This is illustrated in

Utilizing Parallel Lines in Proofs Reasons 1 Given 2 Given 3 If parallel lines cut by transversal, then altemate angles are conguent 4 Transitive property 5 If base angles are congruent, then triangle is isosceles AEK BED 1 2 5 ABE is isosceles BED EBA BAE BAE or Recognizing the altemate interior angles Example Given Prove Circle E

Prove and apply theorems about lines and angles. Include multi-step proofs and algebraic problems built upon these concepts. Examples of theorems include but are not limited to o Vertical angles are congruent. o If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.