Mrs. Welch Math 2 Midterm Review
Opposite reciprocal
Two numbers whose product is -1
Conditions ensuring a parallelogram
(1) opposite sides are parallel (2) the diagonals of a quadrilateral bisect each other
Rotations 180 degrees
(x,y) becomes (-x,-y)
Reflections across the y axis
(x,y) becomes (-x,y)
Reflections across the line y = -x
(x,y) becomes (-y,-x)
Rotations 90 degrees counterclockwise (270 degrees clockwise)
(x,y) becomes (-y,x)
Reflections across the x axis
(x,y) becomes (x,-y)
Rotations 270 degrees counterclockwise (90 degrees clockwise)
(x,y) becomes (y,-x)
Reflections across the line y = x
(x,y) becomes (y,x)
Equation of a circle with center at (a,b) and radius r
(x-a)² + (y-b)²= r²
Slope formula
(y₂- y₁) / (x₂- x₁)
perpendicular bisector of a segment
A line or a line segment that forms a right angle to a segment and contains its midpoint
rhombus
A quadrilateral with all four sides the same length
square
A quadrilateral with all four sides the same length and four right angles
parallelogram
A quadrilateral with opposite sides the same length
rectangle
A quadrilateral with opposite sides the same length and four right angles
kite
A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
right triangle
A triangle with an angle that measures 90 degrees
isoscleles triangle
A triangle with at least two sides the same length
Translations to the right
Add to the x coordinate
Translations up
Add to the y coordinate
Base Angles of Isosceles Triangle
Angles opposite congruent sides of an isosceles triangle are congruent.
Conditions ensuring a square
Consecutive sides of a rectangle are the same length
30°-60°-right angle relationship
For a right triangle with acute angles of measures 30° and 60°, the length of the side opposite the 30° angle is half the length of the hypotenuse. The length of the side opposite the 60° angle is √3 times the length of the side opposite the 30° angle.
45°-45°-right angle relationship
For a right triangle with acute angles of measures 45°, the length of the hypotenuse is √2 times the length of the leg of a right triangle.
congruent figures
Have the same shape and size regardless of position or orientation
Pythagorean Theorem
If the lenghts of the sides of a right triangle are a,b,c, with the side of length c opposite the right angle, then a²+b²=c².
Converse of the Pythagorean Theorem
If the sum of the squares of the lengths of two sides of a triangle equals the square of the length of the third side, then the triangle is a right triangle.
Side-Side-Side (SSS) congruence condition
If three sides of a triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) congruence condition
If two angles and the side between the angles of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) congruence condition
If two sides and the angle between the sides of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.
Opposite Angles Property of Parallelograms
Opposite angles in a parallelogram are congruent.
Translations to the left
Subtract from the x coordinate
Translations down
Subtract from the y coordinate
Conditions ensuring a rectangle
The diagonals of a quadrilateral are the same length
Triangle Inequality
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
Triangle Angle Sum Property
The sum of the measures of the angles is 180 degrees
Quadrilateral Angle Sum Property
The sum of the measures of the angles is 360 degrees
Polygon Angle Sum Property
The sum of the measures of the interior angles where n = the number of sides is (n - 2) x 180 degrees
Distance formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
