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?

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

12

43

5 68 7

• Transversal: a line that intersects two or more coplanar lines at different points.

• < 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

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

White Boards

White Boards

      (c) Write down the values of a and b.

 

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

(Total 6 marks) 

Angles Carousel Question 2

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 = 2303x = y – 50                                    3x + y = 410

(c)     Hence, or otherwise, work out the values of x and y.(Total 6 marks)

Angles Carousel Question 3

Angles Carousel Question 4

Angles Carousel Question 5

Angles Carousel Question 6

CHALLENGE

Challenge 2