Definition
a method of drawing conclusions by going from the specific to the general
What is Inductive Reasoning?
Parallel Lines Postulate
Think about railroad tracks. They are designed to be parallel so that the train can run smoothly. This real-life example illustrates the concept of parallel lines that never intersect.
11) False. Sample: A rectangle with sides of 3 in and 5 in is not a square.
what is If a figure is a rectangle, then it is a square?
v
and
a mathematical statement that has not yet been rigorously proved.
Pythagorean Theorem
If you have a right-angled triangle, such as a ladder leaning against a wall, the theorem helps you determine the length of the ladder (hypotenuse) if you know the height of the wall and the distance of the ladder's base from the wall.
27) 1. ) 3𝑥 + 16 = 2(𝑥 + 6) 1.) Given 2.) 3𝑥 + 16 = 2𝑥 + 12 2.) Distributive property of equality 3.) 𝑥 + 16 = 12 3.) Subtraction property of equality 4.) 𝑥 = −4 4.) Subtraction property of equality You could combine steps 3 and 4 if you prefer.
whAT IS Given: 3𝑥 + 16 = 2(𝑥 + 6) Prove: x = - 4?
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or
any exception to a generalization.
Point, Line, and Plane
Point: A point can be thought of as a location on a map or a dot on a piece of paper. - Line: A line can be represented by the edge of a ruler or a tightrope stretched between two points. - Plane: A plane can be visualized as the surface of a table or a piece of paper.
If a number is not divisible by 2, then it is not even.
WHAT IS Write the contrapositive.
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not
statements that are accepted as true without being proven
what is postulate
Complementary Angles
in a corner of a room, the ceiling meets the wall at a 90-degree angle. If you were to place a piece of molding that splits this angle into two, each of the resulting angles would be complementary (adding up to 90 degrees).
2) If a number is not even, then it is not divisible by two.
WHAT IS 2) Write the inverse.?
p
Number is a whole number
the opposite of the given mathematical statement
what is negation?
Congruence and Similarity
Congruent Figures: Two identical smartphones can be considered congruent because they have the same shape and size. - Similar Figures: Two photographs of the same scene taken from different distances are similar because they have the same shape but different sizes. These examples help illustrate how geometric concepts are applied in everyday life.
False, Not all congruent angles are right angles. A sample counter example would be 2 angles with measures of 25°.
WHAT IS Is the biconditional statement true or false? Explain your reasoning. Two angles are congruent if and only if they are right angles.
r
A number is a rational number