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Transcript of Jose Pablo Reyes. Polygon: Any plane figure with 3 o more sides Parts of a polygon: side – one of...
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Jose Pablo Reyes
Ch. 6 – Polygons and Quadrilaterals
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Polygon: Any plane figure with 3 o more sides
Parts of a polygon:
side – one of the segments that is part of the polygon
Diagonal – a line that connects two vertices that are not a side
Vertex – the point where two segments meet
Interior angle – the angle that is formed inside the polygon by two adjacent sides
Exterior angle – the angle that is formed outside the polygon by two adjacent sides
Describe what a polygon is. parts of a polygon.
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Polygon Examples
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Convex polygon – is a polygon in which all vertices point out
Concave polygon – is a polygon in which at least one angle is pointing into the center of the figure
Equiangular – polygon in which all angles are congruent
Equilateral – polygon in which all sides are congruent
Describe convenx and concave polygons , equilateral and equiangular.
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Convex and Concave, Equilangular and Equilateral polygons – Examples
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Interior angles theorem of quadrilaterals:
Interior angles theorem for quadrilaterals
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Interior angle theorem of a quadrilateral Examples
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Theorem 6-2-4 : If a quadrilateral is a parallelogram its diagonals bisect each other converse: if the diagonals of a quadrilateral bisect each other then it is a parallelogram
Theorem 6-3-2: If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram converse: if in a quadrilateral both pairs of opposite sides are congruent then it is a parallelogram
4 theorems of parallelograms and their converse
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Theorem 6-6-2: If a quadrilateral is a kite, then its diagonals are perpendicularconverse: if in a quadrilateral the diagonals are perpendicular, then it is a kite
Theorem 6-5-2: If the diagonals of a parallelogram are congruent, then it is a rectangleconverse: if a rectangle has congruent diagonals, then it is a parallelogram
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A quadrilateral is a parallelogram if; - opposite sides are parallel - opposite angles are congruent - opposite sides are congruent - adjacent angles are supplementary - diagonals bisect each other
Theorem 6.10:
How to prove a quadrilateral is a parallelogram – Theorem 6.10
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Proving a quadrilateral is a parallelogram Examples
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Squares :4 sided regular
polygon, that has all sides and angles
congruent int. angles = 90
2 pairs of parallel lines
Rhombuses:quadrilateral with 4 congruent sides its diagonals are perpendicular
Rectangles:4 sided polygon with congruent
angles int. angles = 90diagonals are
congruent Two pairs of
parallel lines
Comparing – Rhombuses, Squares and rectangles
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Comparing: Rhombuses, Squares and rectangles – Examples
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Theorem 6-4-3: If a quadrilateral is a rhombus, then it is a parallelogram
Theorem 6-4-4: If a parallelogram is a rhombus, then its diagonals are perpendicular
Theorem 6-4-5: If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles
Rhombus Theorems
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Rhombus Theorems – Examples
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Theorem 6-4-1: If a quadrilateral is a rectangle, then it is a parallelogram
Theorem 6-4-2: If a parallelogram is a rectangle, then its diagonals are congruent
Rectangle Theorems
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Rectangle Theorems – Examples
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Trapezoid: A quadrilateral with one pair of parallel lines, each parallel side is called a base, and the parts that are not parallel are called legs.
Isosceles trapezoid: when the legs are congruent
Theorem 6-6-3: if a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent
Theorem 6-6-4: if a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles
Theorem 6-6-5: a trapezoid is isosceles if and only if its diagonals are congruent
Trapezoid and its theorems
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Trapezoid Theorems – Examples
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Theorem 6-6-6: The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases
Trapezoid mid segment theorem
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Kite: A quadrilateral with two pairs of congruent consecutive sides
Theorem 6-6-1: if a quadrilateral is a kite, then its diagonals are perpendicular
Theorem 6-6-2: if a quadrilateral is a kite, then a pair of opposite angles are congruent
Kite and its Theorems
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Kite – Examples
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To find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus
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3 area postulates and how they are used