Homework Helpers:
What we've learned so far
Quadrilaterals sum to 360 degrees
As every quadrilateral can be made with 2 triangles!
The angles also fit together to make a full revolution (circle)
As every quadrilateral can be made with 2 triangles!
The angles also fit together to make a full revolution (circle)
Trapezoids: Have exactly one set of parallel sides which are not congruent.
Trapezoids can be: Isosceles, Right angled or irregular.
Trapezoids can be: Isosceles, Right angled or irregular.
They have 2 sets of co-interior angles that sum to 180 degrees
Isosceles trapezoids have 2 congruent sides and 2 sets of congruent angles.
Isosceles trapezoids have 2 congruent sides and 2 sets of congruent angles.
Midsegments of a trapezoid: The midsegment of a trapezoid is equal to half the base(s)
So in the diagram below: (18 + 48)/2 so that X would equal 33.
So in the diagram below: (18 + 48)/2 so that X would equal 33.
Parallelograms
Parallelogram properties:
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Rectangles
Rectangles have all the properties of a parallelogram plus:
To prove a rectangle on the coordinate plane we must prove: that it has 2 sets of parallel sides that are perpendicular. (slopes are the negative reciprocal) |
This is a rectangle because it has two sets of parallel sides that are perpendicular to each other.
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Squares
Squares have all the properties of a parallelogram, rectangle and a rhombus
Too prove a square. You must prove that the figure is a rectangle with congruent adjacent sides.
- Four congruent sides
- Diagonals are congruent, perpendicular and bisect the corner angles
- When you add two diagonals you get four congruent, isosceles right triangles
Too prove a square. You must prove that the figure is a rectangle with congruent adjacent sides.
Rhombus
A rhombus has all the properties of a parallelogram and:
To prove a rhombus, you must prove a shape is a parallelogram with congruent sides.
- Diagonals are perpendicular bisectors
- all sides are congruent
- diagonals are angle bisectors
- When you add one diagonal you create two congruent isosceles triangles.
- When you add a second diagonal you create 4 congruent right triangles.
To prove a rhombus, you must prove a shape is a parallelogram with congruent sides.