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SECTION 3-2ANGLES AND PARALLEL LINES
Wednesday, December 14, 2011
ESSENTIAL QUESTIONS
HOW DO YOU USE THEOREMS TO DETERMINE THE RELATIONSHIPS BETWEEN SPECIFIC PAIRS OF ANGLES?
HOW DO YOU USE ALGEBRA TO FIND ANGLE MEASUREMENTS?
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
CORRESPONDING ANGLES POSTULATE
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
CORRESPONDING ANGLES POSTULATE
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF
CORRESPONDING ANGLES IS CONGRUENT.
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
CORRESPONDING ANGLES POSTULATE
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF
CORRESPONDING ANGLES IS CONGRUENT.
∠1 ≅ ∠5
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
ALTERNATE INTERIOR ANGLES THEOREM
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
ALTERNATE INTERIOR ANGLES THEOREM
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF
ALTERNATE INTERIOR ANGLES IS CONGRUENT.
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
ALTERNATE INTERIOR ANGLES THEOREM
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF
ALTERNATE INTERIOR ANGLES IS CONGRUENT.
∠4 ≅ ∠6
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
CONSECUTIVE INTERIOR ANGLES THEOREM
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
CONSECUTIVE INTERIOR ANGLES THEOREM
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF CONSECUTIVE INTERIOR ANGLES IS
SUPPLEMENTARY.
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
CONSECUTIVE INTERIOR ANGLES THEOREM
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF CONSECUTIVE INTERIOR ANGLES IS
SUPPLEMENTARY.
∠4 AND ∠5 ARE SUPPLEMENTARY
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
ALTERNATE EXTERIOR ANGLES THEOREM
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
ALTERNATE EXTERIOR ANGLES THEOREM
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF ALTERNATE EXTERIOR ANGLES IS
CONGRUENT.
Wednesday, December 14, 2011
POSTULATES AND THEOREMS
ALTERNATE EXTERIOR ANGLES THEOREM
IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF ALTERNATE EXTERIOR ANGLES IS
CONGRUENT.
∠2 ≅ ∠7
Wednesday, December 14, 2011
EXAMPLE 1
IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO
YOUR ANSWER.a. m∠2
b. m∠3
c. m∠6
Wednesday, December 14, 2011
EXAMPLE 1
IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO
YOUR ANSWER.a. m∠2
51°; VERTICAL ANGLESWITH ∠4
b. m∠3
c. m∠6
Wednesday, December 14, 2011
EXAMPLE 1
IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO
YOUR ANSWER.a. m∠2
51°; VERTICAL ANGLESWITH ∠4
b. m∠3129°; SUPPLEMENTARY ANGLES WITH ∠4
c. m∠6
Wednesday, December 14, 2011
EXAMPLE 1
IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO
YOUR ANSWER.a. m∠2
51°; VERTICAL ANGLESWITH ∠4
b. m∠3129°; SUPPLEMENTARY ANGLES WITH ∠4
c. m∠651°; ALTERNATE INTERIOR ANGLES WITH ∠4
Wednesday, December 14, 2011
EXAMPLE 2
USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR
THE ANSWER FOR EACH MEASURE.
Wednesday, December 14, 2011
EXAMPLE 2
USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR
THE ANSWER FOR EACH MEASURE.
m∠1 = 125°; VERTICAL
WITH ∠2
Wednesday, December 14, 2011
EXAMPLE 2
USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR
THE ANSWER FOR EACH MEASURE.
m∠1 = 125°; VERTICAL
WITH ∠2m∠3 = 55°; CONSECUTIVE
INTERIOR WITH ∠2
Wednesday, December 14, 2011
EXAMPLE 2
USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR
THE ANSWER FOR EACH MEASURE.
m∠1 = 125°; VERTICAL
WITH ∠2m∠3 = 55°; CONSECUTIVE
INTERIOR WITH ∠2m∠4 = 125°; CONSECUTIVE
INTERIOR WITH ∠3
Wednesday, December 14, 2011
EXAMPLE 2
USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR
THE ANSWER FOR EACH MEASURE.
m∠1 = 125°; VERTICAL
WITH ∠2m∠3 = 55°; CONSECUTIVE
INTERIOR WITH ∠2m∠4 = 125°; CONSECUTIVE
INTERIOR WITH ∠3
m∠5 = 55°; SUPPLEMENTARY WITH ∠4
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
a. IF m∠2 = 2x − 10 AND
m∠6 = x + 15, FIND x.
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
a. IF m∠2 = 2x − 10 AND
m∠6 = x + 15, FIND x.
2x − 10 = x + 15
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
a. IF m∠2 = 2x − 10 AND
m∠6 = x + 15, FIND x.
2x − 10 = x + 15−x −x
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
a. IF m∠2 = 2x − 10 AND
m∠6 = x + 15, FIND x.
2x − 10 = x + 15−x −x +10+10
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
a. IF m∠2 = 2x − 10 AND
m∠6 = x + 15, FIND x.
2x − 10 = x + 15−x −x +10+10
x = 25
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
a. IF m∠2 = 2x − 10 AND
m∠6 = x + 15, FIND x.
2x − 10 = x + 15−x −x +10+10
x = 25
SINCE THE ANGLES ARE CORRESPONDING, THEY ARE CONGRUENT, MEANING THEY ARE
EQUAL.
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
b. IF m∠7 = 4(y − 25) AND
m∠1 = 4y, FIND y.
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
b. IF m∠7 = 4(y − 25) AND
m∠1 = 4y, FIND y.
4(y − 25) + 4y = 180
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
b. IF m∠7 = 4(y − 25) AND
m∠1 = 4y, FIND y.
4(y − 25) + 4y = 1804y − 100 + 4y = 180
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
b. IF m∠7 = 4(y − 25) AND
m∠1 = 4y, FIND y.
4(y − 25) + 4y = 1804y − 100 + 4y = 180
8y − 100 = 180
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
b. IF m∠7 = 4(y − 25) AND
m∠1 = 4y, FIND y.
4(y − 25) + 4y = 1804y − 100 + 4y = 180
8y − 100 = 1808y = 280
Wednesday, December 14, 2011
EXAMPLE 3
USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING.
b. IF m∠7 = 4(y − 25) AND
m∠1 = 4y, FIND y.
4(y − 25) + 4y = 1804y − 100 + 4y = 180
8y − 100 = 1808y = 280
y = 35
Wednesday, December 14, 2011
CHECK YOUR UNDERSTANDING
CHECK OUT PROBLEMS 1-10 ON PAGE 181.
Wednesday, December 14, 2011
PROBLEM SET
Wednesday, December 14, 2011
PROBLEM SET
P. 181 #11-35 ODD
“YOU CAN FOOL TOO MANY OF THE PEOPLE TOO MUCH OF THE TIME.” - JAMES THURBER
Wednesday, December 14, 2011