Download Day 2 notes and assignment

Math 11
Unit 2 - Geometry
Day 2 Notes
Exploring Parallel Lines
Intro Activity
Transversal – a line that intersects two or more other lines at distinct points.
Transversal crossing
two lines
this Transversal
crosses two parallel
lines
... and this one cuts
across three lines
When a transversal intersects two parallel lines, how are the angle measures related?
Interior angles
– any angles formed by a transversal and two parallel lines that lie inside the parallel
lines. (see Ð3, Ð4, Ð5 and Ð6 )
1. Two interior angles on the same side of the transversal will add to 180°. (IASST = 180o)
2. Two interior angles on alternate sides of the transversal will be equal. (alt. int. <s =)
Matty 2012
Math 11
Unit 2 - Geometry
Day 2 Notes
Correspondingl angles
- one interior angle and one exterior angle that are non-adjacent but on the same
side of the transversal. (see Ð1 and Ð5, Ð4 and Ð8, Ð2 and Ð6, Ð3 and Ð7 )
3. Pairs of corresponding angles are always equal.
Vertically opposite angles
- the angles opposite each other when two lines cross.
(see Ð1 and Ð3, Ð2 and Ð4, Ð5 and Ð7, Ð6 and Ð8 )
4. Pairs of vertically opposite angles are always equal.
***These 4 above laws are crucial to understand for the rest of the unit**
Activity #2:
Grab a laptop in a group of two and check out the following websites and experiment with
the animations to help you understand the terms and rules of parallel lines:
1. Terms: http://tube.geogebra.org/m/153296
2. More on terms and Relationships: http://tube.geogebra.org/m/575951
Now try some of these examples and determine the unknown angle measurements:
1.
x
w
y
Ðx=
Ðw=
120°
Ðy=
Matty 2012
Math 11
Unit 2 - Geometry
55°
Day 2 Notes
Ða=
2.
Ðb=
d
a
Ðc=
e
f
b
112°
c
Ðd =
Ðe=
Ðf=
3.
Ð b=
d
Ð c=
c
b
Ð d=
48°
e
g
Ð e=
f
Ð f=
Ð g=
Assignment 2.2
1. Complete the sentences with the correct word: always, sometimes, or never.
Parallel lines are __________________________ the same distance apart.
Parallel lines ______________________________ intersect.
Parallel lines are ___________________________ cut by a transversal.
Parallel lines that are cut by a transversal _____________________ form right angles.
Matty 2012
Math 11
Unit 2 - Geometry
Day 2 Notes
2. Use a pencil to thicken one set of parallel lines in this pattern.
3. Determine the measure of ABF.
4. Determine the values of a, b, and c.
5. Are BD and FE parallel? Explain how you know.
d
y
6. Use the following figure to the right to answer questions:
t
a) Is line d a transversal? Why or why not?
b) Is line y a transversal?
c) Is line t a transversal? Why or why not?
d) Is line r a transversal?
Matty 2012
r