Hon Geom Drill #2.03 11/11/14 Use the picture and locate all the
corresponding angles, same side interior angles, alternate interior angles, and alternate exterior angles
1 2
34
5
7
6
8
Hon Geom Drill #2.03 11/11/14 Name all angles that must be congruent to
angle 2
1 2
34
5
7
6
8
Find the value of x or y
61
x
Find the value of x or y
60
x
Write the converse
If two lines are perpendicular to the same line, then the two lines are parallel
State the Postulate or theorem that justifies
each statement 18064.1 mm
pk .2
1. In the diagram of movie theater seats, the incline of the floor, f, is parallel to the seats, s.
If mÐ1 = 68°, what is x?
2. In the diagram, roads a and b are parallel.
What is the measure of ÐPQR?
In the diagram of the gate, the horizontal bars are parallel and the vertical bars are parallel. Find x and y. 3. x= 4. y=
||AG CJ|| .AD FJ
Use the diagram of a staircase railing for Exercises 4 and 5.
and
Choose the best answer.
4.Which is a true statement about the measure of ÐDCJ?
A It equals 30°, by the Alternate Interior Angles Theorem.
B It equals 30°, by the Corresponding Angles Postulate.
C It equals 50°, by the Alternate Interior Angles Theorem
D It equals 50°, by the Corresponding Angles Postulate.
5. Which is a true statement about the value of n?
F It equals 25°, by the Alternate Interior Angles Theorem.
G It equals 25°, by the Same-Side Interior Angles Theorem.
H It equals 35°, by the Alternate Interior Angles Theorem.
J It equals 35°, by the Same-Side Interior Angles Theorem.
Are These Lines Parallel?
t
a
b140º40º
Are These Lines Parallel?
t
a
b140º
40º
Are These Lines Parallel?
t
a
b80º
80º
Are These Lines Parallel?
t
a
b
70º
70º
Yes or No!!Are the converses of the
corresponding angles postulate, alternate int. angles thm, alt. Ext. angles thm and same side interior angles thm true?
Yes or No!!Are the converses of the
corresponding angles postulate, alternate int. angles thm, alt. Ext. angles thm and same side interior angles thm true?
OBJECTIVETo PROVE THAT LINES ARE PARALLEL.
Converse of the Corresponding Angle post
If two lines are cut by a transversal such that corresponding angles are congruent, then two lines are parallel.
Converse of the Alternate Interior Angle Theorem
If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
Converse of the Same Side Interior Angle Theorem
If two lines are cut by a transversal such that same side interior angles are supplementary, then the lines are parallel.
STATE EARLIER THEOREM
t
a
b
THEOREM
If two lines are perpendicular to the same line, then the lines are parallel to each other.
NEW THEOREMIf a || b
and
a || c,
then?????????
THEOREM
If two lines are parallel to the same line, then the lines are parallel to each other.
Conclusions 1) State the converses 2) If two lines are perpendicular to the same line then…
3) If two lines are parallel to the same line then...
