1.2.2c3.notebook
September 11, 2013
September 9, 2013
nigeB
Agenda: 1. Warm up
STM & CYU pg. 34
2. 1.2.2 #s 1 ­ 3
3. Parallel Lines and Transversals
1.2.2c3.notebook
September 11, 2013
Summarize the Mathematics pg. 34
Given: <DBA = <CBD
D
A
a. What can you conclude about these two angles?
B
E
C
b. What can you conclude about the other angles in the diagram?
c. What mathematical facts did you use to help prove your statements in Parts a and b?
Were these facts definitions, postulates, or theorems?
d. Describe the relationship between lines AC and DE.
CYU pg. 34
In the diagram at the right, Lines AD and BE intersect
at point C and m<ECD = m<D.
a. Is m<ACB = m<D? If so, prove it. If not, give a counterexample.
b. Is m<A = m<D. If so, prove it. If not, give a counterexample.
1.2.2c3.notebook
September 11, 2013
1. In the preceding diagram, the angles at each point of
intersection are numbered so that they can be easily identified.
a. What pairs of angles, if any, appear to be equal in measure?
b. What angle pairs appear to be supplementary? (*** Remember*** Supplementary angles need not be a linear pair or side by side.)
c. Draw another pair of parallel lines and a transversal with a slope different from the one above. Number the angles as in the figure above.
i. Do the same pairs of numbered angles appear equal in measure?
ii. Do the same pairs of numbered angles appear to be supplementary?
1.2.2c3.notebook
September 11, 2013
Angles that are in the same relative position with respect to each
parallel line and the transversal are called corresponding angles.
In the diagram to the right or previous page, angles 1 and 5 are
corresponding angles; similarly, angles 3 and 7 are corresponding
angles.
2. Examine the diagram you drew for Part c of Problem 1.
a. Name two pairs of corresponding angles, other than angles
1 and 5 or angles 3 and 7. Were those corresponding angles
among the pairs of angles that you thought had equal measure?
b. Suppose m<1 = 1230. Find the measure of as many other angles as you can in your diagram.
1.2.2c3.notebook
September 11, 2013
3. Descriptive names are also given to other pairs of angles formed by a transversal and two parallel lines. In the diagram below, m ll n and t is a transversal intersecting m and n.
a. For each pair of angles named below,
describe how the pair can be identified in a diagram.
Then give one more example of such a pair.
i. Interior angles on the same side of the transversal: <4 and <5
ii. Exterior angles on the same side of the
transversal: < 2 and <7
iii. Alternate interior angles: < 4 and <6
iv. Alternate exterior angles: < 1 and <7
b. Identify a relationship that seems to exist for each type of angle pair named in Part a. Write your observations in if­then form, beginning each statement as follows. If two parallel lines are cut by a transversal, then...
i. If two parallel lines are cut by a transversal, then
ii. If two parallel lines are cut by a transversal, then
iii. If two parallel lines are cut by a transversal, then
iv. If two parallel lines are cut by a transversal, then
1.2.2c3.notebook
September 11, 2013
Parallel Lines and Transversal Worksheet Options for Part 1
1. Corresponding Angles (Equal in Measure)
2. Exterior Angles on the same side (Supplementary Angles)
3. Interior Angles on the same side (Supplementary Angles)
4. Alternate Interior Angles ( Equal in measure)
5. Alternate Exterior Angles (Equal in measure)