GEOMETRY CHAPT 1
Terms
undefined, object
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- FOUR STEP PLAN to solving a mathematical problem
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1.EXPLORE the problem
2.PLAN the solution
3.SOLVE the problem
4.EXAMINE the solution - line segment
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has a definite beginning POINT
and a definite end POINT. - AREA of a rectangle
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the number of square units to cover the figure. Like carpet
AREA= L multiplied by width
area = length x width
ANSWER ALWAYS GIVEN IN SQUARE UNITS - noncollinear
- points NOT on the same line
- CONDITIONAL STATEMENTS
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AN IF-THEN STATEMENT LIKE A GURANTEE.
HAS 2 PARTS;HYPOTHESIS& CONCLUSION
FOLLOWING IF= HYPOTHESIS
FOLLOWING THEN=CONCLUSION
IF "IF" IS NOT PART OF THE HYPOTHESIS, THEN "THEN" IS NOT PART OF THE CONCLUSION! -
collinear
- on the same line.
- CONTRAPOSITIVE of the conditional
- FIRST TAKE THE CONVERSE OF THE CONDITIONAL(EXCHANGE THE HYPOTHES AND CONCLUSION) THEN NEGATE BOTH THE HYPOTHESIS (IF) AND THE CONCLUSION (THEN)
- INDUCTIVE REASONING
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MAKE A CONCLUSION BASED ON A PATERN OF EXAMPLES OR PAST EVENTS.
EXAMPLE: DARK CLOUDS AND YOU REASON THERE WILL BE A STORM!
LOOK AT A PATERN OF NUMBERS TO FIND THE NEXT NUMBER IN A SEQUENCE. - COPLANAR
- POINTS THAT LIE ON THE SAME PLANE AS THE FIRST 3 POINTS
- CONJECTURE (CON JEC TURE)
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A CONCLUSION OR EDUCATED GUESS
IT IS BASED ON INDUCTIVE REASONING.
SOMETIMES CORRECT SOMETIMES
NOT.
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POSTULATE 1-1
HOW TO DETERMINE A LINE -
TWO POINTS DETERMINE A UNIQUE LINE.
- LINE
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A SEARIES OF AN INFINITE NUMBER OF POINTS THAT EXTENDS WITHOUT END IN BOTH DIRECTIONS.
can be named by a single lower case letter a or by 2 points on the line AB
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POSTULATE 1-3
THE PLANE - THREE NONCOLLINEAR POINTS DETERMINE A UNIQUE PLANE.
- COUNTEREXAMPLE
- WHEN CONJECTURE (EDUCATED GUESS) IS INCORRECT
- CONVERSE of a conditional statement
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substitute the hypothesis (if)
for the conclusion(then) of a
statement.
CONDITIONAL: IF A FIGURE IS A TRIANGLE, THEN IT HAS 3 ANGLES
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CONVERSE: IF A FIGURE HAS 3 ANGLES, THEN IT IS A TRIANGLE - POINT
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THE BASIC UNIT OF GEOMETRY
IT HAS NO SIZE
IT IS NAMED USING CAPITAL LETTERS .A -
POSTULATE 1-2
INTERSECTING LINES -
IF TWO LINES INTERSECT; THEN
THEIR INTERSECTION IS A POINT. - ray
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definite starting POINT and extends indefinately in the direction of the arrow
A .-------------->
THE STARTING POINT IS CALLED THE ENDPOINT
IT IS LABELED USING THE ENDPOINT FIRST, THEN ANOTHER POINT ON THE RAY.
THE FIRST LETTER TO APPEAR IS THE ENDPOINT EG AB - PERIMETER
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THE DISTANCE AROUND THE outside of a figure
perimeter= length+width=length=width or
P=2(l)=2(w) - POSTULATE (POS TUL ATE)
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THE FACTS ABOUT GEOMETRY THAT ARE ACCEPTED AS TRUE.
THE FOUNDATION OF GEOMETRY - PLANE
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FLAT SURFACE EXTENDS IN ALL DIRECTIONS FOR ANY THREE NON-
COLLINEAR POINTS.
THERE IS ONLY ONE PLANE THAT CONTAINS ALL THREE POINTS - INVERSE of the conditional
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take the conditional then, negate (make negative or opposite) both the hypothesis(if) and the conclusion(then)
CONDITIONAL;
if it is raining, then it is cloudy.
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INVERSE:
if it is not raining, then it is not cloudy - AREA of a parallelogram
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area of parallelogram is the
BASE x height
(not side x height)*****
**height of parallelogram is determined by right
triangle.***