Square
What makes a polygon regular?
All sides are congruent, and all angles are congruent
is a rectangle a square?
sometimes
What is the definition of a rhombus
A parallelogram with all sides congruent
is a trapezoid a parallelogram?
No, a trapezoid can only have one set of opposite parallel sides
A quadrilateral with two pairs of consecutive congruent sides, where opposite sides are not congruent
What is the definition of a square?
a parallelogram with congruent sides and congruent angles
What is the definition of a rectangle?
A parallelogram with 4 congruent sides
A parallelogram with 4 right angles
Both a rhombus and a kite have perpendicular diagonals, how do you differentiate them?
rhombuses are parallelograms with all sides congruent, kite do not have all sides congruent nor are they parallelograms. Prove whether it is or isn't a parallelogram or whether opposite sides are congruent.
What is the definition of a trapezoid? An isosceles trapezoid?
A quadrilateral with only one set of opposite parallel sides. A trapezoid with congruent legs.
List all the properties of a kite
diagonals are perpendicular, and only one set of opposite angles are congruent
Given the image, what is the area of the polygon?
392.5 in.^2
What properties are unique to a rectangle (ignoring square)?
All angles congruent, and diagonals congruent
How would you prove that a quadrilateral is a rhombus? In coordinate geometry?
parallelogram/quadrilateral with all sides congruent (distance formula on side lengths), parallelogram with perpendicular diagonals (prove parallelogram and opposite reciprocal slopes of diagonals), parallelogram with opposite angles bisected by diagonals (you will not be asked to do this in coordinate geometry at the moment)
List all the properties of an isosceles trapezoid
Only one set of opposite parallel sides, legs are congruent, base angles are congruent, and diagonals are congruent.
how would you prove on coordinate geometry, that a quadrilateral is a kite?
Distance formula on all sides
Given the vertices A(2, 4), B(5, 3), C(4, 0), and D(1, 1). Is the quadrilateral formed a square? How do you know?
Yes
[Insert explanation]
How would you prove that a quadrilateral is a rectangle? How would you prove that it's also not a square?
List formulas and steps in detail.
1. parallelogram(opp sides congr., opp angles congru, opp sides parallel, consec int angles supplementary, same opp sides parallel and congr., diagonals bisect) and diagonals are congr.. quadrilateral with all angles congruent/90 degrees.
2. prove it's not a rhombus (all sides not congruent, diagonals not perpendicular, diagonals don't bisect opp angles)
Given the vertices A(-1, 5), B(3, 0), C(1, -1), and D(-3, 4), is the shape formed a rhombus? How do you know?
No
[Insert explanation]
i.e. all sides are not congruent (with work showing such), therefore it is not a rhombus by definition
Given the vertices A(2, 6), B(-3, 0), C(3, -4), and D(5, 4), what is the most specific name for the quadrilateral? How do you know?
Isosceles Trapezoid
[Insert explanation]
Given the vertices A(-5, 7), B(2, 6), C(5, -3), and D(-4, 0), is the quadrilateral formed a kite? How do you know?
Yes
[Insert explanation]
Daily Double!
Given the image, what error(s) was(were) made?
How should it be written?
Image is wrong, missing labels, no explanation, conclusion not proven/correct
Fill in the missing information
CPCTC
Given the rhombus, what are its angle measurements?
Angle ABC = 6, angle ADC = 6, angle BCD = 174, angle CAB = 174
Find the area of the trapezoid
36
Find the perimeter of the kite
4(13)1/2 + 8(5)1/2