Warm Up: Read In Lesson 1.3.1, you used the properties of supplementary angles and straight angles to show that vertical angles are congruent.  Today you will use a tile pattern to investigate other angle pair relationships. 3 1-81. Marcos was walking home after school when he noticed a pattern of parallelogram tiles on the wall of a building.  Marcos saw lots of angle pair relationships in the tile pattern, so he decided to copy it into his notebook. What is your job for this problem? Recorder/Reporter Facilitator Resource Manager Task Manager 4

1.3.2 Angles Formed by Transversals HW: 1-87 through 1-92 1.3.2  Angles Formed by Transversals August 29, 2018

Objectives CO: SWBAT transform and use angle pair relationships. LO: SWBAT use vocabulary such as vertical angles, linear pair, complementary angles, and corresponding angles.

Together: (students use tracing paper) http://technology. cpm You have the beginning of Marcos’s diagram.  This type of pattern is sometimes called a tiling.  In this tiling, a parallelogram is copied and translated to fill an entire page without gaps or overlaps. Recall that two polygons are congruent if there is a sequence of rigid transformations that carries one polygon onto the other.  Describe three different sequences of rigid transformations that can be used to carry one parallelogram onto another in Marcos’s diagram. 180 rotation, translation, reflections over x and y axis Consider the angles inside a single parallelogram from the pattern.  Which angles are congruent?  How can you justify your claim? Opposite angles Since each parallelogram is a translation of another, what can be stated about the angles in the rest of Marcos’ tiling?  Use tracing paper to determine which angles must be congruent.  Color all angles that must have equal measure the same color. They are congruent to the same ones in the original polygon  What about relationships between lines?  Can you identify any lines in the diagram that must be parallel?  Mark all the lines on your diagram with the same number of arrows to show which lines are parallel. All vertical lines are parallel and all horizontal lines are parallel

1-82. Julia wants to learn more about the angles in Marcos’s diagram and has decided to focus on just a part of his tiling.  An enlarged view of that section is shown, with some points and angles labeled. In partners A line that crosses two or more other lines is called a transversal.  In Julia’s diagram, which line is the transversal?  Which lines are parallel?   Trace ∠x on tracing paper and shade its interior.  Then translate ∠x by sliding the tracing paper along the transversal until it lies on top of another angle and matches it exactly.  Which angle in the diagram corresponds with ∠x?  In this diagram, ∠x and ∠b are called corresponding angles because they are in the same position at two different intersections of the transversal.  What is the relationship between angles x and b?  Explain how you know. 

1-83. CORRESPONDING ANGLES FORMED BY PARALLEL LINES The corresponding angles in Julia’s diagram in problem 1-82 are congruent because they were formed by translating a parallelogram. Name all of the other pairs of corresponding angles in Julia’s diagram from problem 1-82.  (Round Robin) Suppose b = 60⁰.  Use what you know about angle pair relationships to determine the measures of all of the other angles in Julia’s diagram.  (Round Robin)

1-84. ARE THEY ALWAYS CONGRUENT? So far you have investigated transversal lines that cross pairs of parallel lines.  However, transversal lines can cross any pair of lines, not just parallel lines. Frank wonders whether corresponding angles are always congruent.  For parts (a) through (d) below, use tracing paper to determine whether corresponding angles are congruent.  Then, if you have enough information, determine angle measures x and y and state the angle pair relationship. team e. Answer Frank’s question: Are corresponding angles always congruent?  If not, when are they congruent? PROGRESS CHART on board when they finish each part