Chapter 6 Review (Geo) (2009)

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Chapter 6 Chapter 6 ReviewReview

Need:Need:-Notes-Notes-Conjecture List-Conjecture List

© 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.

© EQUIANGULAR POLYGON © EQUIANGULAR POLYGON CONJECTURECONJECTURE© EQUIANGULAR POLYGON © EQUIANGULAR POLYGON CONJECTURECONJECTUREThe measure of one angle in any equiangular polygon can be found with the expression:

© 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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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!!!

OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS

© KITE DIAGONALS CONJECTURE© KITE DIAGONALS CONJECTURE© KITE DIAGONALS CONJECTURE© KITE DIAGONALS CONJECTURE

Diagonals of a kite are perpendicular

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

OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS

© KITE ANGLES CONJECTURE© KITE ANGLES CONJECTURE© KITE ANGLES CONJECTURE© KITE ANGLES CONJECTURE

Non-vertex angles of a kite are congruent

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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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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TRAPEZOIDTRAPEZOIDTRAPEZOIDTRAPEZOIDA quadrilateral with exactly one pair of parallel sidesA quadrilateral with exactly one pair of parallel sides

OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS

© TRAPEZOID CONSECUTIVE ANGLE © TRAPEZOID CONSECUTIVE ANGLE CONJECTURECONJECTURE© TRAPEZOID CONSECUTIVE ANGLE © TRAPEZOID CONSECUTIVE ANGLE CONJECTURECONJECTUREConsecutive angles between bases are supplementary

OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS

© ISOSCELES TRAPEZOID CONJECTURE© ISOSCELES TRAPEZOID CONJECTURE© ISOSCELES TRAPEZOID CONJECTURE© ISOSCELES TRAPEZOID CONJECTUREBase angles in an isosceles trapezoid are congruent

OBSERVATIONSOBSERVATIONSOBSERVATIONSOBSERVATIONS

© ISOSCELES TRAPEZOID DIAGONAL © ISOSCELES TRAPEZOID DIAGONAL CONJECTURECONJECTURE© ISOSCELES TRAPEZOID DIAGONAL © ISOSCELES TRAPEZOID DIAGONAL CONJECTURECONJECTURE

Diagonals in an isosceles trapezoid are congruent

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.

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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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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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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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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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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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

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

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°°

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

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

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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