Download transversals and angle pair properties 14

transversals and angle pair properties 14­15.notebook
Geo opener
Learning
Targets
October 17, 2014
10­17­14
transversals and special angle pair theorems
Use a geometry term to describe the special angle pairs that are formed
1) <1 and <4
Vertical Angles
2) <3 and <4
Linear Pair
3) <1 and <8
Alt. Ext. Angles
4) <5 and <4
Alt. Int. Angles
5) <1 and <5
Corresponding Angles
6) <6 and <4
Consec. Int. Angles
Word Bank
transversals and angle pair properties 14­15.notebook
October 17, 2014
transversals and angle pair properties 14­15.notebook
October 17, 2014
line a is parallel to line b. Line c is a transversal
12
0o
60 o
What do you notice about the following types of angles
a 120
120o 60o
o021
o
120o 60o
b
c
Vertical Angles
Alt. Int. Angles
Alt. Ext. Angles
Linear Pair
Corresponding Angles
Consec. Int. Angles
line a is Not parallel to line b. Line c is a transversal
What do you notice about the following types of angles120
120o 60
60oo
a
o
b
60o
o
Vertical Angles
Linear Pair
021
c
Alt. Int. Angles
Alt. Ext. Angles
Corresponding Angles
Consec. Int. Angles
transversals and angle pair properties 14­15.notebook
October 17, 2014
Corresponding Angles Postulate
by construction
Boxes
Corr. are iff the 2 lines cut by the transversal are //.
Alternate Interior Angles Theorem
Alternate interior angles are congruent if and only if the two lines cut by the transversal are parallel.
A.I.A are iff the 2 lines cut by the transversal are //.
If a//b, then a
2
1
4
3
5
b
6
8
7
c
Boxes
shorthand???
shorthand???
Corresponding angles are congruent if and only if the two lines cut by the transversal are parallel.
proof?
AIA are transversals and angle pair properties 14­15.notebook
October 17, 2014
Alternate Exterior Angles Theorem
A.E.A a
boxes
shorthand???
Alternate Exterior angles are congruent if and only if the two lines cut by the transversal are parallel.
boxes
Consecutive interior angles are supplementary if and only if the two lines cut by the transversal are parallel.
shorthand???
Consecutive Interior Angles Theorem
C.I.A ar
transversals and angle pair properties 14­15.notebook
m< 1 = 500
October 17, 2014
Find the measure of the rest of the angles
m< 2 =
1 2
4 3
m< 3 =
m< 4 =
56
8 7
m< 5 =
m<6 =
m< 7 =
m< 8 =
In the figure at the right p is parallel to q. Find the measure of each angle. <1=78, <2=47
1. m<3 4 6
2. m<4
3. m<5 3
5
4. m<6
5. m<7 1
9
q
6. m<8 7. m<9 8. m<10
p
10
2 8
7