Properties of Equality
Explain what an angle bisector is.
An angle bisector divides an angle into two equal angles.
What properties determine an isosceles trapezoid?
An isosceles trapezoid has one pair of opposite sides are parallel, and one pair of NON-parallel sides are congruent.
What properties help us determine if a quadrilateral is a parallelogram?
A quadrilateral is a parallelogram if there are two pairs of opposite sides parallel.
Explain how we can determine if two segments are congruent using coordinate geometry.
We will determine the length of two segments using the distance formula to prove if the segments are congruent. If the segments have equivalent lengths, then the segments are congruent.
Explain the transitive property.
If a=b and b=c then a=c.
Describe what a segment bisector and midpoint have in common. How is a median related?
A segment and a midpoint divides a segment into two equal segments. A median connects a midpoint to the opposing vertex.
What properties determine a right trapezoid?
What properties determine an equilateral triangle?
An equilateral triangle has 3 equivalent sides.
Explain how you would prove that a quadrilateral is a square.
4 distance formula to show 4 equal lengths. 2 distance of diagonal to show diagonals are equal in length. (may also use 2 slopes to show 1 pair adjacent sides are perpendicular, or 2 slopes of diagonals to prove diagonals are perpendicular.)
Explain the subtraction property.
Subtract part from whole to get missing part. AC - BC = AB
Explain the difference between parallel and perpendicular lines.
Parallel lines have equivalent slopes, whereas perpendicular lines have slopes which are negative reciprocals.
Explain how a rhombus, rectangle and square are all parallelograms.
A rhombus, rectangle and square are all parallelograms because they all have 2 pairs of opposite sides parallel and congruent.
Explain why a square is a rectangle but a rectangle is not a square.
A square is a rectangle because it has two pairs of opposite sides congruent and diagonals are congruent, but rectangle is not a square because a rectangle does not have 4 congruent sides.
Explain how you would prove that a quadrilateral is a trapezoid and NOT a parallelogram.
4 slope to prove there are two pairs of opposite sides parallel (equal slopes).
Explain the addition property.
Add two parts together to determine the entire length. AB + BC = AC
Explain the difference between congruent and equal.
Congruent means the segments are equal in length but in different positions. Equal means the exact same length.
Explain what a rhombus and square have in common but a rectangle differs.
A rhombus and square both have perpendicular diagonals, but a rectangle does not.
Explain why a square is a rhombus but a rhombus is not a square.
A square is a rhombus because they both have 4 equal sides in length, but a rhombus is not a square because a rhombus does not have adjacent sides perpendicular whereas a square does.
Explain how you would prove a rhombus.
4 distance formula to show 4 equal lengths. 2 distance of diagonal to show diagonals are NOT equal in length. (may also use 2 slopes to show 1 pair adjacent sides are NOT perpendicular; or 2 slopes of diagonals to show diagonals are perpendicular)
Explain the difference between the associative property and commutative property of addition/multiplication.
Associative property allows you to add/multiply terms regardless of how they are grouped. (a+b)+c=a+(b+c). Commutative property allows you add/multiply terms regardless of order ab=ba.
Explain which angles can be used to prove parallel lines.
If two lines form congruent alternate interior angles OR congruent corresponding angles, then the lines are parallel.
Explain if it is possible for a quadrilateral to be an isosceles right trapezoid.
No, it is not possible for a quadrilateral to be an isosceles right trapezoid because an isosceles trapezoid has 2 pairs of non-parallel sides are congruent and base angles are congruent. A right trapezoid has 2 pairs of right angles; therefore, if base angles are also right, then all four angles will be right, which means the quadrilateral will be a rectangle.
Explain the difference between an isosceles, an equilateral and a right triangle.
An isosceles triangle has two pairs of ≅ sides and 2 base angles ≅ . An equilateral triangle has 3 ≅ sides and 3 ≅ angles. A right angle has one pair of adjacent sides perpendicular forming a 90 degree angle.
Distance is represented by "d" - used to find length. Midpoint is represented by "M" - used to determine the point which divides the segment equally. Slope is represented by "m" - which is used to determine the steepness.