Download - 3004 provinglineparral
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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
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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
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Find the value of x or y
61
x
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Find the value of x or y
60
x
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Write the converse
If two lines are perpendicular to the same line, then the two lines are parallel
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State the Postulate or theorem that justifies
each statement 18064.1 mm
pk .2
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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?
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2. In the diagram, roads a and b are parallel.
What is the measure of ÐPQR?
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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=
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||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.
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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.
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Are These Lines Parallel?
t
a
b140º40º
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Are These Lines Parallel?
t
a
b140º
40º
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Are These Lines Parallel?
t
a
b80º
80º
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Are These Lines Parallel?
t
a
b
70º
70º
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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?
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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?
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OBJECTIVETo PROVE THAT LINES ARE PARALLEL.
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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.
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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.
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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.
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STATE EARLIER THEOREM
t
a
b
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THEOREM
If two lines are perpendicular to the same line, then the lines are parallel to each other.
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NEW THEOREMIf a || b
and
a || c,
then?????????
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THEOREM
If two lines are parallel to the same line, then the lines are parallel to each other.
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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...