1. Things Needed Today (TNT):
Math CC7/8 – Sept. 19
Things Needed Today (TNT):
Math Notebook/Pencil
Shapes & Designs 3.4
Book if you want to follow along
Math Notebook
Topic: Parallel Lines & Transversals
Homework: p. 78 #17, 39 & Worksheet

2. What’s Happening?
Warm Up
Lesson- S&D 3.4!

3. Warm-Up End What is a regular polygon? What is an irregular polygon?
1 minute
WRITE down each problem & SOLVE
Show ALL your work & THINKING
What is a regular polygon?
What is an irregular polygon?
What is the sum of the interior angles in a triangle.
What is the sum of the exterior angles of a pentagon?
End

4. Check your work in a different colored pen or color pencil
Answers to Warm Up
Check your work in a different colored pen or color pencil
Polygon with the same side lengths and the same angle measure.
Polygon where not all the sides are the same lengths and not all the angles are the same measure.
180 degrees
360 degrees

5. Opposite angles of any parallelogram are congruent.
Parallelogram: a four-sided flat shape with opposite sides parallel. Opposites sides are equal length and opposite angles are equal.
Pg. 9
Opposite angles of any parallelogram are congruent.
Refer to handout on the table

7. 2. What pattern seems to relate the measures of consecutive angles in any parallelogram?
Consecutive angles of any parallelogram are supplementary (add to 180° degrees).

8. Explain how you know the measures without using tools.
Use labsheet 3.4 B
Explain how you know the measures without using tools.
Possible Explanation:
Due to the fact that opposite angles of parallelograms are congruent, angle D is 135° since it is opposite of angle B.
Also, consecutive angles of any parallelogram are supplementary (added to 180°), you could subtract 135° from 180° and find angle C (45°).

9. Use labsheet 3.4 B Hint: What do you know about parallelogram? Hmmm
Did you notice that when two lines intersect, four angles are formed? The opposite pairs of angles are called vertical angles.
Vertical angles: each pair of opposite angles made by two intersecting lines.

10. A line that intersects 2 other lines is called a transversal.
Problem 3.4…continued
Take Notes C
A line that intersects 2 other lines is called a transversal.
1. From your work in Questions A & B, what can you say about the measures of the 8 angles formed by a transversal and 2 parallel lines?
A transversal through a set of parallel lines forms
congruent angles.
(a, c, e, and h are congruent)
(b, d, f, and g are congruent) a a b b L 1 d c c d e e f f L g g h 2 h t

11. Explain how you know the measures of the labeled angles!
Problem 3.4…continued
2. Suppose the measure of angle f is 80º. What are the measures of the other labeled angles?
Explain how you know the measures of the labeled angles!
Angles a, c, e, & h
are 100º.
Angles b, d, f, & g
are 80°. a b L 1 c d L e f 2 g h
Possible explanation:
Transversal t is going through the parallel lines (L1 & L2) which allows you to know that angle g is congruent to angle f which is 80°. ` t

12. For example, in Question C, angles f and g are vertical angles.
Problem 3.4…continued
Take Notes
Did you notice that when two lines intersect, four angles are formed? The opposite pairs of angles are called vertical angles.
Vertical angles: each pair of opposite angles made by two intersecting lines.
For example, in Question C, angles f and g are vertical angles.
1. Name the other pairs of vertical angles in the figure of question C.
Vertical angles:
a and c
b and d
e and h
f and g a b d c e f g h t

13. 2. Supplementary angles are any adjacent pair:
Name the pairs of supplementary angles in the figure below.
What is true about the measures of any vertical angle pair?
2. Supplementary angles are any adjacent pair:
a and b, b and c, c and d, a and d, e and f, f and h, g and h, and e and g.
Vertical angles are always congruent!
If a and c are vertical, they have a common supplement b, so they must be the same measure. a b d c e f g h

14. BAC = 155º
x + (6x + 5) = 180
7x + 5 = 180
7x = 175
x = 25
6x + 5 =155°
EAB = DAC = 25°
CAE = BAD = 180°

15. Homework If time start your HW p
Homework If time start your HW p. 78 #17, 39 & Worksheet (Angle Relationships)