chapter 6 review (geo) (2009)
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LAST NIGHT’S HWLAST NIGHT’S HWLAST NIGHT’S HWLAST NIGHT’S HW
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Chapter 6 Chapter 6 ReviewReview
Need:Need:-Notes-Notes-Conjecture List-Conjecture List
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© POLYGON SUM CONJECTURE© POLYGON SUM CONJECTURE© POLYGON SUM CONJECTURE© POLYGON SUM CONJECTUREThe sum of all the angles in an n-gon (any polygon) is (n–2)180.
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© EQUIANGULAR POLYGON © EQUIANGULAR POLYGON CONJECTURECONJECTURE© EQUIANGULAR POLYGON © EQUIANGULAR POLYGON CONJECTURECONJECTUREThe measure of one angle in any equiangular polygon can be found with the expression:
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© POLYGON EXTERIOR ANGLE © POLYGON EXTERIOR ANGLE CONJECTURECONJECTURE© POLYGON EXTERIOR ANGLE © POLYGON EXTERIOR ANGLE CONJECTURECONJECTUREThe sum of the exterior angles in any polygon is 360 degrees
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ReviewReviewReviewReview
KITEKITEKITEKITEA quadrilateral with exactly 2 pairs of distinct congruent consecutive sidesA quadrilateral with exactly 2 pairs of distinct congruent consecutive sides
Vertex Vertex AnglesAngles
Non-vertex Non-vertex AnglesAngles NO PARALLEL
SIDES!!!
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© KITE DIAGONALS CONJECTURE© KITE DIAGONALS CONJECTURE© KITE DIAGONALS CONJECTURE© KITE DIAGONALS CONJECTURE
Diagonals of a kite are perpendicular
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© KITE DIAGONAL BISECTOR CONJ.© KITE DIAGONAL BISECTOR CONJ.© KITE DIAGONAL BISECTOR CONJ.© KITE DIAGONAL BISECTOR CONJ.
The diagonal connecting the vertex angles bisectors the non-vertex angle diagonal
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© KITE ANGLES CONJECTURE© KITE ANGLES CONJECTURE© KITE ANGLES CONJECTURE© KITE ANGLES CONJECTURE
Non-vertex angles of a kite are congruent
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© KITE ANGLE BISECTOR CONJECTURE© KITE ANGLE BISECTOR CONJECTURE© KITE ANGLE BISECTOR CONJECTURE© KITE ANGLE BISECTOR CONJECTUREThe vertex angles of a kite are bisected by the vertex diagonal
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ReviewReviewReviewReview
TRAPEZOIDTRAPEZOIDTRAPEZOIDTRAPEZOIDA quadrilateral with exactly one pair of parallel sidesA quadrilateral with exactly one pair of parallel sides
Base Base AnglesAngles
Base Base AnglesAngles
BaseBase11
BaseBase22
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ReviewReviewReviewReview
TRAPEZOIDTRAPEZOIDTRAPEZOIDTRAPEZOIDA quadrilateral with exactly one pair of parallel sidesA quadrilateral with exactly one pair of parallel sides
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© TRAPEZOID CONSECUTIVE ANGLE © TRAPEZOID CONSECUTIVE ANGLE CONJECTURECONJECTURE© TRAPEZOID CONSECUTIVE ANGLE © TRAPEZOID CONSECUTIVE ANGLE CONJECTURECONJECTUREConsecutive angles between bases are supplementary
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© ISOSCELES TRAPEZOID CONJECTURE© ISOSCELES TRAPEZOID CONJECTURE© ISOSCELES TRAPEZOID CONJECTURE© ISOSCELES TRAPEZOID CONJECTUREBase angles in an isosceles trapezoid are congruent
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© ISOSCELES TRAPEZOID DIAGONAL © ISOSCELES TRAPEZOID DIAGONAL CONJECTURECONJECTURE© ISOSCELES TRAPEZOID DIAGONAL © ISOSCELES TRAPEZOID DIAGONAL CONJECTURECONJECTURE
Diagonals in an isosceles trapezoid are congruent
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© TRIANGLE MIDSEGMENT CONJECTURE© TRIANGLE MIDSEGMENT CONJECTURE© TRIANGLE MIDSEGMENT CONJECTURE© TRIANGLE MIDSEGMENT CONJECTUREThe midsegment is parallel to the third side and half the length of the third.
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OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS
© TRAPEZOID MIDSEGMENT CONJECTURE© TRAPEZOID MIDSEGMENT CONJECTURE© TRAPEZOID MIDSEGMENT CONJECTURE© TRAPEZOID MIDSEGMENT CONJECTUREThe midsegment of a trapezoid is parallel to the bases and its length is the average of the two bases.
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ReviewReviewReviewReview
PARALLELOGRAMPARALLELOGRAMPARALLELOGRAMPARALLELOGRAMA quadrilateral with 2 pairs of opposite sides that are parallel.A quadrilateral with 2 pairs of opposite sides that are parallel.
Opposites sides are parallel
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ReviewReviewReviewReview
PARALLELOGRAMPARALLELOGRAMPARALLELOGRAMPARALLELOGRAMA quadrilateral with 2 pairs of opposite sides that are parallel.A quadrilateral with 2 pairs of opposite sides that are parallel.
Opposites sides are congruent
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ReviewReviewReviewReview
PARALLELOGRAMPARALLELOGRAMPARALLELOGRAMPARALLELOGRAMA quadrilateral with 2 pairs of opposite sides that are parallel.A quadrilateral with 2 pairs of opposite sides that are parallel.
Opposites angles are congruent
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ReviewReviewReviewReview
PARALLELOGRAMPARALLELOGRAMPARALLELOGRAMPARALLELOGRAMA quadrilateral with 2 pairs of opposite sides that are parallel.A quadrilateral with 2 pairs of opposite sides that are parallel.
Consecutive angles are supplementary
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ReviewReviewReviewReview
PARALLELOGRAMPARALLELOGRAMPARALLELOGRAMPARALLELOGRAMA quadrilateral with 2 pairs of opposite sides that are parallel.A quadrilateral with 2 pairs of opposite sides that are parallel.
Diagonals bisect each other
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What is a Parallelogram?What is a Parallelogram? Opposite sides are Opposite sides are
parallelparallel Opposite sides are Opposite sides are
congruentcongruent Opposite angles are Opposite angles are
equalequal Consecutive angles Consecutive angles
supplementarysupplementary Diagonals bisect Diagonals bisect
eachothereachother
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What is a Rectangle?What is a Rectangle?
Rectangles are Rectangles are special special parallelogramsparallelograms Has all the properties Has all the properties
of a parallelogramof a parallelogram All angles are All angles are
congruentcongruent Each angle is 90Each angle is 90°°
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What is a Rhombus?What is a Rhombus?
Rectangles are Rectangles are special special parallelogramsparallelograms Has all the properties Has all the properties
of a parallelogramof a parallelogram
Has four congruent Has four congruent sidessides
Sometimes called a Sometimes called a diamonddiamond
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What is a Square?What is a Square? Squares are special Squares are special
parallelogramsparallelograms Has all the properties of Has all the properties of
a parallelograma parallelogram A square is a kind of A square is a kind of
rectanglerectangle Each angle is 90Each angle is 90°°
A square is also a A square is also a special rhombusspecial rhombus All sides are congruentAll sides are congruent
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What is a Square?What is a Square? A square is an A square is an
equilateral rectangleequilateral rectangle
A square is an A square is an equiangular rhombusequiangular rhombus
A regular quadrilateralA regular quadrilateral
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HOMEWORKHOMEWORKPacket