Unit 1: Reasoning in Geometry
Definition of inductive reasoning
What is a conjecture based on observing patterns in the data?
Definition of vertical angles
What are non-adjacent angles formed by two straight lines that are congruent
Definition of a rigid transformation
What is a transformation that does not affect the size or shape of the object moved?
Definition of an isosceles triangle
What is a triangle that has two congruent sides?
Definition of a parallelogram
What is a quadrilateral with two pairs of parallel sides
The two parts of a good definition
What is classification and differentiation?
Midpoint formula between 2 coordinates
What is (x1 + x2/2, y1 + y2/2)
The rule for a point's reflection across the y-axis
What is (x, y) --> (-x, y)
True or False: Side lengths 4, 6, and 10 make a triangle.
What is false
The name of the shape whose diagonals are congruent and bisect each other and has 4 right angles
What is a rectangle/square
A conditional statement that is true both ways
What is biconditional statement?
Explain how to determine if two lines are perpendicular on the coordinate plane
What is the two lines are perpendicular if their slopes are a negative reciprocal of each other
The rule for a 270 degree rotation
What is (x,y) --> (y,-x)
The length of the hypotenuse of a right triangle if its legs are 15 and 13 (square root form)
What is square root of 394 ... Work: 132 = 169 and 152 = 225, 169 + 225 = 394. To get length you get square root of 394
True or False: A trapezoid is always an isosceles trapezoid
What is false
True or False: Multiples of 3 always fluctuate between odd and even
What is true (Multiples of 3: 3, 6, 9, 12, 15... they fluctuate between odd and even)
Midpoint between (3, -8) and (4, -11)
What is (3.5, -9.5) ... Work: (3+4/2, -8 + -11/2) = (7/2, -19/2) = (3.5, -9.5)
Equation of y=x2 if it was reflected across the x-axis
What is y=-x2
Find the perimeter of a right triangle that has a hypotenuse that measures 25 inches and a leg that measures 7 inches.
What is 56 inches ... Work: 72 + b2 = 252 , 49 + b2 = 625, b2 = 576, b = 24. To get perimeter you add 7 + 24 + 25 to get 56 inches
Explain how using the slope can help determine what kind of quadrilateral is made by 4 ordered pairs
What is calculating slope can determine if the lines in the quadrilateral are parallel/perpendicular
What is a rigorous argument with loopholes or assumptions to justify that something is true or not true?
Two angles are complementary; one measures 2x + 9 and the other measures 3x + 10. Find value of x
What is x = 14.2 ... Work: 2x + 3x + 9 + 10 = 90, 5x + 19 = 90, 5x = 71, x = 14.2
Equation of a graph y = |x| if it was translated 5 units right and 10 units up.
What is y = |x-5| + 10
Name the type of triangle (right, obtuse, or acute) with side lengths 5, 7, and 8.
What is an acute triangle ... Work: 52 + 72 > 82, since the sum of shorter sides' squares is greater than the square of the longest side it is acute
Name the most specific name of a quadrilateral with points (5,6), (0,7), (-6,6), and (-2,4)
What is an irregular quadrilateral (Reasoning: Quadrilateral has no congruent diagonals, no congruent sides, and no pairs of sides are parallel/perpendicular)