 TEKS Focus:  6)(A) Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angle formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems.  (1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.  (1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace.

Vocabulary TermSymbolNameDefinition Coplanar lines that never intersect. Lines that intersect at a 90 ⁰ or right angle. Lines that are not coplanar, are not parallel, and do not intersect. Planes that do not intersect. Parallel Lines || Perpendicular Lines Skew Lines Parallel Planes T none || A B C D E F G

Segments or rays are parallel, perpendicular, or skew if the lines that contain them are parallel, perpendicular, or skew. Helpful Hint

If a transversal is perpendicular to two parallel lines, all eight angles are congruent. Helpful Hint Remember that postulates are statements that are accepted without proof. Remember

Identify each of the following. A. a pair of parallel segments B. a pair of skew segments C. a pair of perpendicular segments D. a pair of parallel planes LM ||QR KN and PQ NS  SR plane NMR || plane KLQ

An Ames room is a distorted room that is used to create an optical illusion. Two people the same height, standing in different parts of the room, can appear to be different sizes. Identify each of the following. A. a pair of parallel segments B. a pair of skew segments C. a pair of perpendicular segments CD ||GH CD is skew to FG DH  GH

Vocabulary TermDefinitionExample A line that intersects two or more coplanar lines at two different points. Angles that lie on the same side of the transversal and in corresponding positions. Nonadjacent interior angles that lie on opposite sides of the transversal. Nonadjacent exterior angles that lie on opposite sides of the transversal. Interior angles that lie on the same side of the transversal. Also called consecutive interior angles. Transversal The transversal t intersects lines r and s forming 8 angles. Corresponding Angles  1 and  5  3 and  7  2 and  6  4 and  8 Alternate Interior Angles  3 and  6  4 and  5 Alternate Exterior Angles  1and  8  2 and  7 Same-side Interior Angles  3and  5  4 and  6

Notice that the numbers on this diagram are different from the previous diagram. Don’t memorize the vocabulary words by #s!

Give all examples of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles  1 &  5;  2 &  6;  3 &  7;  4 &  8 D. same-side interior angles  3 &  5 or  4 &  6  1 &  7 or  2 &  8  3 &  6 or  4 &  5

Give one example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles  1 and  3 D. same-side interior angles  2 and  7  1 and  8  2 and  3

To determine which line is the transversal for a given angle pair, locate the line that connects the vertices. Helpful Hint

Identify the transversal and classify each angle pair. A.  1 and  3 B.  2 and  6 transversal l corr.  s transversal n alt. int  s

Identify the transversal and classify the angle pair  2 and  5 in the diagram. transversal n same-side int.  s. Identify the transversal and classify the angle pair  4 and  6 in the diagram. transversal m alternate ext.  s.

 EXTRA EXAMPLES NOT USED IN COMPOSITION BOOK FOLLOW.  ALSO REMEMBER TO LOG-ON TO YOUR PEARSON ACCOUNT TO LOOK AT OTHER EXAMPLES BEFORE BEGINNING THE ON-LINE HW AND THE WRITTEN HW.

Identify each of the following. a. a pair of parallel segments b. a pair of skew segments d. a pair of parallel planes c. a pair of perpendicular segments BF || EJ BF and DE are skew. BF  FJ plane FJH || plane BCD