WEDNESDAY, OCTOBER 5
WARM­UP:
WHAT IS THE APPROXIMATE LENGTH OF
PQ WITH ENDPOINTS P(2,5) AND Q(­4,8)?
CORRECT HOMEWORK
PRACTICE 2.2A # 1 ­ 8
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1) IF YOUR BODY TEMPERATURE IS 103 , THEN YOU HAVE A FEVER.
2) IF A DEER HAS WHITE FUR AND PINK EYES, THEN IT IS AN ALBINO.
3) IF YOU WANT THAT CD, THEN I'LL BUY IT FOR YOU.
4) IF A VEHICLE IS A PICKUP TRUCK, THEN IT HAS A HIGH UTILITY VALUE.
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5)
CONVERSE: IF THE TEMPERATURE OF WATER IS BELOW 0 C, THEN IT IS FROZEN.
INVERSE: IF WATER IS NOT FROZEN, THEN ITS TEMPERATURE IS NOT BELOW 0 C.
CONTRAPOSITIVE: IF THE TEMPERATURE OF WATER IS NOT BELOW 0 C, THEN IT IS NOT FROZEN.
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6)
CONVERSE: IF X = 2, THEN X+3=5
INVERSE: IF X + 3 = 5, THEN X = 2
CONTRAPOSITIVE: IF X = 2, THEN X + 3 = 5
4
7)
IF­THEN: IF IT RAINS, THEN IT POURS.
(FALSE)
CONVERSE: IF IT POURS, THEN IT RAINS.
(TRUE)
INVERSE: IF IT DOESN'T RAIN, THEN IT DOESN'T POUR.
(TRUE)
CONTRAPOSITIVE: IF IT DOESN'T POUR, THEN IT DOESN'T RAIN.
(FALSE)
5
8)
IF­THEN: IF FOUR POINTS ARE COLLINEAR, THEN THEY ARE COPLANAR.
(TRUE)
CONVERSE: IF FOUR POINTS ARE COPLANAR, THEN THEY ARE COLLINEAR.
(FALSE)
INVERSE: IF FOUR POINTS ARE NOT COLLINEAR, THEN THEY ARE NOT COPLANAR.
(FALSE)
CONTRAPOSITIVE: IF FOUR POINTS ARE NOT COPLANAR, THEN THEY ARE NOT COLLINEAR.
(TRUE)
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CONDITIONAL: IF X, THEN Y.
CONVERSE:
INVERSE:
CONTRAPOSITIVE:
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IF­THEN :
IF A POLYGON IS EQUILATERAL, THEN IT IS REGULAR. CONVERSE:
IF A POLYGON IS REGULAR, THEN IT IS EQUILATERAL.
INVERSE:
IF A POLYGON IS NOT EQUILATERAL, THEN IT IS NOT REGULAR.
CONTRAPOSITIVE: IF A POLYGON IS NOT REGULAR, THEN IT IS NOT EQUILATERAL.
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IF THEN: IF AN ANIMAL IS A WHALE,
THEN IT IS A MAMMAL.
CONVERSE: IF AN ANIMAL IS A MAMMAL,
THEN IT IS A WHALE.
INVERSE: IF AN ANIMAL IS NOT A WHALE, THEN IT IS NOT A MAMMAL.
CONTRAPOSITIVE:
IF AN ANIMAL IS NOT A MAMMAL,
THEN IT IS NOT A WHALE.
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A CONDITIONAL STATEMENT AND ITS CONTRAPOSITIVE ARE EITHER BOTH TRUE OR BOTH FALSE. SIMILARLY, THE CONVERSE AND THE INVERSE OF A CONDITIONAL STATEMENT ARE EITHER BOTH TRUE OR BOTH FALSE. PAIRS OF STATEMENTS SUCH AS THESE ARE CALLED EQUIVALENT STATEMENTS. IN GENERAL, WHEN TWO STATEMENTS ARE BOTH TRUE OR BOTH FALSE, THEY ARE CALLED EQUIVALENT STATEMENTS.
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PERPENDICULAR LINES
IF TWO LINES INTERSECT TO FORM A RIGHT ANGLE, THEN THEY ARE PERPENDICULAR LINES.
THE DEFINITION CAN ALSO BE WRITTEN USING ITS CONVERSE:
IF TWO LINES ARE PERPENDICULAR, THEN THEY INTERSECT TO FORM A RIGHT ANGLE.
l
line l line m
m
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USE THE DIAGRAM SHOWN. DECIDE WHETHER EACH STATEMENT IS TRUE. EXPLAIN YOUR ANSWER USING DEFINITIONS YOU HAVE LEARNED.
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BICONDITIONAL STATEMENTS
WHEN A CONDITIONAL STATEMENT AND ITS CONVERSE ARE BOTH TRUE, YOU CAN WRITE THEM AS A SINGLE BICONDITIONAL STATEMENT. A BICONDITIONAL STATEMENT IS A STATEMENT THAT CONTAINS THE PHRASE "IF AND ONLY IF" .
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REWRITE THE FOLLOWING DEFINITIONS AS A BICONDITIONAL:
1) AN ANGLE WITH A MEASURE BETWEEN
90 AND 180 IS CALLED OBTUSE.
AN ANGLE IS OBTUSE IFF ITS MEASURE IS BETWEEN 90 AND 180 .
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2) TWO ANGLES ARE A LINEAR PAIR IF THEY ARE ADJACENT ANGLES WHOSE NONCOMMON SIDES ARE OPPOSITE RAYS
TWO ANGLES ARE A LINEAR PAIR IFF THEY ARE ADJACENT ANGLES WHOSE NONCOMMON SIDES ARE OPPOSITE RAYS.
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3) COPLANAR POINTS ARE POINTS THAT LIE IN THE SAME PLANE.
POINTS ARE COPLANAR IFF THEY LIE IN THE SAME PLANE.
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4) AN ANGLE WITH A MEASURE OF 90
IS A RIGHT ANGLE.
AN ANGLE IS A RIGHT ANGLE IFF ITS MEASURE IS 90 .
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PRACTICE 2.2A
# 9 ­ 22
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