Geometry Ch. 7 & 9 Flashcards
diagonal of a polygon
a diagonal of a polygon is a line that connects two non-consecutive vertices
sum of the angles of a quadrilateral
the sum of the angles of a quadrilateral is 360°
rectangle
a rectangle is equiangular, all angles equal 90°
all rectangles are paralellograms, so their diagonals bisect each other
parallelogram
- the opposite sides are parallel
- the opposite sides are equal
- the diagonals of a parallelogram bisect each other
if any one of these are true for a quadrilateral, then it must be a parallelogram
square
a square has equal sides and angles
all squares are parallelograms, so their diagonals bisect each other
rhombus
a rhombus has all equal sides (not necessarily equal angles) *all squares are rhombuses, but not all rhombuses are squares
all rhombuses are parallelograms, so their diagonals bisect each other
Area Postulate
- congruent triangles have equal areas
- the area of a polygon is the sum of its non-overlapping parts
Area of a rectangle
Area of a rectangle is b ∙ h
Area of a square
Area of a square is s²
Area of a triangle
The area of a triangle is ½(b ∙ h)
Triangles with equal bases and equal heights have equal areas. Congruent triangles also have equal areas.
Area of a parallelogram
The area of a parallelogram is (b ∙ h)
Trapezoid
A trapezoid is a quadrilateral with at least one pair of parallel sides
Area of a trapezoid
The area of a trapezoid is ½h(a + b). a and b are the length of the parallel sides
Pythagorean Theorem
The side lengths of a right triangle can be determined by a² + b² = c²
(c is the hypoteneus– the side opposite the right angle)
True or False: two quadrilaterals with the same perimeter have the same area as well
False, see the example below
Perimeter
To calculate perimeter, add the length of all the sides
