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# GEOMETRY CHAPT 1

## Terms

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FOUR STEP PLAN to solving a mathematical problem
1.EXPLORE the problem
2.PLAN the solution
3.SOLVE the problem
4.EXAMINE the solution
line segment
has a definite beginning POINT
and a definite end POINT.
AREA of a rectangle
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
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
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)
A CONCLUSION OR EDUCATED GUESS
IT IS BASED ON INDUCTIVE REASONING.
SOMETIMES CORRECT SOMETIMES
NOT.
POSTULATE 1-1

HOW TO DETERMINE A LINE
TWO POINTS DETERMINE A UNIQUE LINE.
LINE
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
POSTULATE 1-3

THE PLANE
THREE NONCOLLINEAR POINTS DETERMINE A UNIQUE PLANE.
COUNTEREXAMPLE
WHEN CONJECTURE (EDUCATED GUESS) IS INCORRECT
CONVERSE of a conditional statement
substitute the hypothesis (if)
for the conclusion(then) of a
statement.
CONDITIONAL: IF A FIGURE IS A TRIANGLE, THEN IT HAS 3 ANGLES
=========================
CONVERSE: IF A FIGURE HAS 3 ANGLES, THEN IT IS A TRIANGLE
POINT
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
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
THE DISTANCE AROUND THE outside of a figure
perimeter= length+width=length=width or
P=2(l)=2(w)
POSTULATE (POS TUL ATE)
THE FACTS ABOUT GEOMETRY THAT ARE ACCEPTED AS TRUE.
THE FOUNDATION OF GEOMETRY
PLANE
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
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.
=====================
INVERSE:
if it is not raining, then it is not cloudy
AREA of a parallelogram
area of parallelogram is the
BASE x height
(not side x height)*****
**height of parallelogram is determined by right
triangle.***

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