Math Journal 6

polygons A polygon is a figure that is close, has segments that does not intercept and the segments united forms a vertex.

Parts of a Polygon Vertex is the point were two segments meets in a polygon. Leg is the segment in a polygon. Diagonal is a line connecting two angles and isn't a side. Interior angle; angle form by two adjacent side and its inside the polygon. Exterior angle; angle form by two adjacent sides and its outside the polygon.

Part of polygon examples Vertex Exterior Angles Diagonals Legs Interior angles

Compare and contrast convex and concave The only difference between a concave and a convex is that all figures are convex and the concave is that one angle is going inside the figure. The only similarity is that depending on the amount of angles they will have the same area.

Examples of a concave and a convex polygon

Equilateral and equiangular The difference between equilateral and equiangular is that equilateral the sides are congruent and in a equiangular the angles of the polygon are congruent The only similarity is that they form a parallelogram.

Examples of Equilateral and equiangular

Interior angle theorem of a polygon To find the angles of a regular polygon you need to do this formula= polygon = (N - 2) x 180° (N=the number of angles in the polygon) As we know the triangle has 3 angles so we do the formula (n-2) x 180, (3-2)x180 so 1x180 and the triangle is 180 As we know this is a heptagon so we do the formula (n-2) x 180, (7-2) x 180, 5x180 = 900 As we know this is a dodecagon so we do the formula (n-2) x 180, (12-2)x 180, 10 x 180 = 1800

the 4 theorems of parallelograms and their converse Theorem 6-2-1 If a quadrilateral is a parallelogram, then its opposite sides are congruent Theorem 6-2-2 If a quadrilateral is a parallelogram then its opposite angles are congruent Theorem 6-2-3 If a quadrilateral is parallelogram, then its consecutive angles are supplementary Theorem 6-2-4 If a quadrilateral is parallelogram, then its diagonals bisect each other.

Examples of theorem 6-2-1

Examples of theorem 6-2-2

Examples of theorem 6-2-3 17 76 104 163 35 145

Examples of theorem 6-2-4

how to prove that a quadrilateral is a parallelogram Both opposite sides are congruent Both opposite angles are congruent Both opposite sides are parallel Consecutive angles are supplementary One pair of congruent and parallel sides When the diagonals bisect

Examples

Compare and contrast a rhombus with a square with a rectangle The rectangle has 4 right angles and diagonals are congruent The rhombus has 4 congruent sides and diagonals bisect perpendicular The square is both a rectangle and a rhombus, it is equidistant and equiangular and diagonals are congruent and bisect perpendicularly.

Quadrilateral Parallelogram Rhombus Square Rectangle

Describe a trapezoid A quadrilateral with one pair of parallel sides Base angles- angles whose common side is a base. Isosceles trapezoid- has 2 congruent legs > >>

Theorems of Trapezoid If legs are parallel the base angles are congruents In a isosceles trapezoid it has two congruent diagonals Trapezoid midsegment theorem,

Examples of trapezoid

Trapezoid midsegment If we do the formula that is (b1+b2)/2 we well get the midsegment, the top base line is 4 and the down base line is 6 so we if put them in the formula it would look like this (4+6)/2 and the answer is 5 The top base line is 1 and the bottom base line is 9 so we do the formula and we get the 5 as the answer As the top basement line is 14.3 and the bottom base line is 3.9 and we do the formula we will get 9.1 as the answer.

Describe a kite 2 pairs of congruent consecutive sides. Perpendicular diagonals. 1 pair of congruent angles.

Examples of a kite