Logic & Reasoning
_________ reasoning is based on patterns, not facts
Inductive
Which property is described by the following:
congruent segments subtracted from congruent segments are congruent
Subtraction Property
What is the image of the point (-2, 6) after a translation left 1 unit and up 3 units?
(-3, 9)
Using point-slope form, write an equation for the line that passes through the points (3, -6) and (1, 2)
y + 6 = -4(x - 3)
y - 2 = -4(x - 1)
Find the midpoint given the line segment with endpoints (-5, 6) and (3, 8)
Midpoint = (4, 7)
State the contrapositive:
If an animal is a cat, then it has whiskers.
If an animal does not have whiskers, then it is not a cat.
Which property is described by the following:
a segment or angle is always congruent to itself
Reflexive Property
What is the image of the point (1, -7) after it has been reflected over the x-axis?
(1, 7)
Solve the system of equations:
y = x
-2x + 4y = 16
x = 8
y = 8
Find a counterexample to show that the conjecture is false:
If n is a real number, then n2 > n
n = 1/2
If the conditional form of a statement is true, which other condition must also be true?
Contrapositive
Which theorem is described below:
if a point is a ____, it splits a segment into two congruent segments
Midpoint Theorem
The image of the point (3, -5) after a translation is (-2, 4). Find the coordinate of the image of the point (5, 2) under the same translation.
(0, 11)
Using point-slope form, write an equation for the line perpendicular to y=3x-7 going through (-8, 9)
y - 9 = -1/3(x + 8)
A triangle has side lengths 14, 21, and x.
What are the restrictions on x?
7 < x < 35
Is the following conclusion valid?
GIVEN: If Leo goes to the beach, he will wear sunscreen.
--> Leo is wearing sunscreen.
CONCLUSION: Leo is at the beach.
NOT valid (law of detachment)
True or False?
the perpendicular lines theorem states that all right angles are congruent
False
(it states the perpendicular lines form right angles)
What is the image of the point (1, 3) after a reflection over the y-axis and then a rotation of 180 degrees counterclockwise?
(1, -3)
Solve the system of equations:
-5x - y = 9
3x - 5y = 17
x = -1
y = -4
A regular quadrilateral and a regular triangle have the same perimeter. The sides of the triangle are 5 inches longer than those of the quadrilateral.
Find the perimeter.
60 in
What is the truth value of (~p ∨ q) ∧ r if
--> p is true, q is false, and r is true
False
Another name for the 3rd Angle Theorem is...
The No Choice Theorem
If 2 angles of one triangle are congruent to 2 angles of another, then the third angles of the triangles are congruent
When A(4, 3) is reflected in a line, its image is A'(-2, 1). Find the equation of the line of reflection, using point-slope form.
y - 2 = -3(x - 1)
Solve the system of equations:
y = -3x2 + 5x + 23
x + y = 14
x = -1, 3
y = 15, 11
The supplement of an angle is 10 more than 3 times the measure of the complement.
Find the degree measure of the supplement.
130 degrees