QUICK REVIEW 1 2 3 4 5 6 7

Transversal Parallel lines Non-Parallel lines transversal transversal A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. transversal Parallel lines Non-Parallel lines transversal

interior exterior exterior INTERIOR –The space INSIDE the 2 lines EXTERIOR -The space OUTSIDE the 2 lines exterior exterior

Special Angle Relationships Interior Angles 1 4 2 6 5 7 8 3

Special Angle Relationships Exterior Angles 1 4 2 6 5 7 8 3

Special Angle Relationships WHEN THE LINES ARE PARALLEL 1 4 2 6 5 7 8 3 ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Corresponding Angles are CONGRUENT If the lines are not parallel, these angle relationships DO NOT EXIST.

Let’s Practice 1 4 2 6 5 7 8 3 120° 60° 60° 120° Find all the remaining angle measures. 120° 60° 60° 120°

Another practice problem 40° Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 120°

3.5 Using Properties of Parallel Lines 1 2 3 4 5 6 7

Standard/Objectives: Use properties of parallel lines in real-life situations. Construct parallel lines using a straight edge and a compass.

Theorem 3.11 about Parallel Lines IF : THEN: k r m m k 8 Book: If two lines are parallel to the same line, then they are parallel to each other. In other words: If k is parallel to m and m is parallel to r, then k is parallel to r.

Theorem 3.12 about Perpendicular Lines IF : THEN: m k k m r 8 Book: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. In other words: If k is perpendicular to r and m is perpendicular to r, then k is parallel to m.

Why is the top step in a ladder parallel to the floor? What do we know about a ladder? Each step is parallel to the one before. The bottom step is parallel to the floor. Then the top step is also parallel to the floor.

Determine which lines, if any, must be parallel in the diagram Determine which lines, if any, must be parallel in the diagram. Explain your reasoning. SOLUTION Lines p and q are both perpendicular to s, so by Theorem 3.12, p || q. Also, lines s and t are both perpendicular to q, so by Theroem 3.12, s || t.

3. yes; Lines Perpendicular to a Use the diagram at the right. 3. Is b || a? Explain your reasoning. 4. Is b c? Explain your reasoning. ANSWER 3. yes; Lines Perpendicular to a Transversal Theorem. 4. yes; c || d by the Lines Perpendicular to a Transversal Theorem, therefore b c by the Perpendicular Transversal Theorem.