3.1/3.2 Identify Pairs of Lines and Angles for Parallel and Non-Parallel Lines with a Transversal

3.1-3.2 Transversals and Parallel Lines Shanghai Temperature In 1990, Shanghai’s average temperature was 18.4 C and in 2013 was 19.3 C. If this was a linear relationship, what would be an equation to represent this relationship? Things to consider: When is t=0? What is the temperature at t=0? What is the temperature increasing by each year? THIS IS COMPLETED IN PAIRS or GROUPS

Parallel and Perpendicular Postulates If you have a line and a point, P, not on that line, then there is 1 line parallel and 1 line perpendicular through P.

Parallel and Perpendicular Prep 1 2 3 4 5 6 8 7

< 1, <5 -corresponding angles <1, <8 - alternate exterior angles <3, <6 - alternate interior angles. <3,<5 -consecutive interior angles 4 7 1 2 3 5 6 8 Transversal: a line that intersects two or more coplanar lines at different points.

Theorems/Postulates Post 15: Corresponding Angles Postulate: If 2 lines are cut by a transversal, the the pairs of corresponding angles are congruent. THEOREMS 3.1-3: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. the pairs of alternate exterior angles are congruent. the pairs of consecutive interior angles are supplementary

Angle Relationships

Whiteboards

Whiteboards

Solving for X x=65 X=56 X=48

White Boards

White Boards

Angles Carousel Question 1 In the diagram AB and CD are parallel. (a)     Write down the value of x. Give a reason for your answer (b)     Work out the value of y. Give a reason for your answer Not drawn accurately       (c) Write down the values of a and b.   (Total 6 marks)  

Angles Carousel Question 2

Angles Carousel Question 3 The diagrams show a trapezoid and a parallelogram. (a)     Use the trapezoid to explain why         2x + y = 180 (b)     The parallelogram can be used to form another equation connecting x and y. Write down the correct equation. 3x + y = 130                                  3x + y = 230 3x = y – 50                                    3x + y = 410 (c)     Hence, or otherwise, work out the values of x and y. (Total 6 marks)

Angles Carousel Question 4

Angles Carousel Question 5

Angles Carousel Question 6

CHALLENGE

Challenge 2