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Learn about polygons, vertices, diagonals, convex, concave, equiangular, equilateral, interior angles, quadrilaterals, parallelograms, proving parallelograms, rhombus, square, rectangle, trapezoid, & kite theorems.
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Journal 6 Cristian Brenner
Polygons • A polygon is a close figuire with straight sides that the line dont interset each other. With three or more segments
Parts of a Polygon • Vertex: the vertex is where the segments of the polygon unite. • Diagonals: are the segments that go from one vertex to the opposite vertex
Convex, Concave • For a concave polygon the vertice are all facing outside and do not go in the figuire like a cave. • In the convex all the vertices are facing out not in, the opposite of the concave
Equiangular, Equilateral • Equilateral: This word is for when a polygon has all it sides congruent. • Equiangular: When a polygons angles are all congruent. • When a polygon is both it is a regular polyon if not it is irregular
Interior angles of Polygons • This theorem says that that the sum of the interior angles of a convex is (n-2)180 (optional)and the answer divided by the number of sides to see how much is each angle.
6-2-1 • If a quadrilateral is a parallelogram then its opposite sides are congruent • Converse: If its opposite sides are congruent then its a parallelogram
6-2-2 • If a quadrilateral is a parallelogram, then its a opposite angles are congruent. • Converse: If opposite angles are congruent then the quadrilateral is a parallelogram
6-2-3 • If a quadrilateral is a parallelogram, Then its consecutive angles are supplementary • If the consecutive angles a of a quadrilateral are supplementery, then it is a parallelogram
6-2-3 If parallelogram then If parallelogram then If parallelogram then
6-2-4 • If a quadrilateral is a parallelogram the its diagonals bisect each other • If diagonals bisect each other then its a parallelogram
Prove quadrilateral is parallelogram • You can know this when: • Opposite angles are congruent • Diagonals bisect • Opposite sides are parallel and congruent • Consecutive angles are supplementary
Rhombus, Square, Rectangle • The rhombus is somelike a square. All sides are congruent but angles change. It has all the characteristics of a parallelogram • The rectangle changes in lenghts measure but all the angles are congruent as in the square. It has all the characteristics of a parallelogram
Rhombus Theorem • 6-4-3 • If a quadrilateral is a rhombus, then it is a parallelogram • 6-4-4 • If a parallelogram is a rhombus, then its diagonals are perpendicular • 6-4-5 • If a parallelogram is a rhombus then each diagonal bisects a pair of oppsite angles
Rectangle Theorem • 6-4-1 • If a quadrilateral is a rectangle, then it is a parallelogram • 6-4-2 • If a parallelogram is a rectangle the its diagonals are congruent.
6-4-1 rectangle rectangle rectangle
Square • It is a parallelogram which all its features are congruent
Trapezoid • A polygon that has only two pair of parallel segments and sometime it is iscoceles, and when it is isco. Base angles and non parallel sides are congruent
Trapezoid Theorems • 6-6-3 • If a quadrilateral is and iscoceles trapezoid, then each pair of base angles are congruent • 6-6-5 • A trapezoid is iscoceles if and only if its diagonals are congruet
Kite • It has two congruent adjecent sides and the diagonals are perpendicular. Two pair of congruent sides. • Theorems: • 6-6-1 • If a quadrilateral is a kite, then its diagonals are perpendicular • 6-6-2 • If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
