Inductive Reasoning
This type of reasoning uses patterns and observations to make a general conclusion.
What is inductive reasoning?
In the statement “If a polygon has three sides, then it is a triangle,” the “if” part is called the __________.
What is the hypothesis?
What is the converse of a conditional statement?
What is switching the hypothesis and conclusion?
This type of reasoning uses facts, definitions, and rules of logic to reach a conclusion.
What is deductive reasoning?
A triangle has this sum of interior angles.
What is 180°?
A statement says: “All quadrilaterals with four congruent sides are squares.” This shape proves the statement false.
What is a rhombus?
In the statement “If a polygon has three sides, then it is a triangle,” the “then” part is called the __________.
What is the conclusion?
What is the converse of:
“If a polygon has three sides, then it is a triangle.”
What is If a polygon is a triangle, then it has three sides?
If m∠A = 75° and “If an angle is less than 90°, then it is acute,” what can you conclude about ∠A?
What is ∠A is acute?
A quadrilateral has this sum of interior angles.
What is 360°?
If you notice that the sum of the interior angles increases by 180° each time a side is added, you are making a __________ based on a pattern.
What is a conjecture?
Identify the hypothesis in this statement: “A rectangle must have four congruent angles.”
What is A polygon is a rectangle?
A biconditional combines a conditional and its converse using these words.
What is if and only if?
If a figure is a square, then it has four sides.
If a figure has four sides, then it is not a triangle.
What conclusion follows?
What is If a figure is a square, then it is not a triangle?
A pentagon has this sum of interior angles.
What is 540°?
A table shows:
Using the pattern, what is the sum of the interior angles of an 8-sided polygon?
What is 1080°?
Identify the conclusion in this statement: “A rectangle must have four congruent angles.”
What is The polygon has four congruent angles?
Rewrite as a biconditional:
“If M is the midpoint of AB, then AM = MB.”
What is M is the midpoint of AB if and only if AM = MB?
In the Law of Syllogism, if
p → q and q → r,
then you can conclude this.
What is p → r?
A hexagon has this sum of interior angles.
What is 720°?
From the table of polygon angle sums, this conjecture is supported:
A. Doubling the number of sides doubles the sum of the interior angles.
B. The sum of the interior angles increases by 180° with each additional side.
What is B?
Determine the truth value:
“If a parallelogram has four right angles, then it is a rectangle.”
What is True?
From the biconditional “Two lines are parallel if and only if they do not intersect,” give one true conditional implied by the statement.
What is If two lines are parallel, then they do not intersect?
Let
p = “a polygon has three sides”
q = “a polygon is a triangle”
r = “the interior angles of a polygon sum to 180°”
If p → q and q → r are true, then if p is true, r is __________.
What is true?
In the triangle pattern from the quiz, the vertex angles go 90°, 89°, 88°, 87°, 86°… What is the next vertex angle?
What is 85°?