Topic 6 Vocabulary Geometry

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45 Terms

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Polygon

A plane figure that meets the following conditions:

  • It’s formed by three or more segments called sides, such as no two sides with common e splints are collinear

  • Each side intersects exactly two other sides, one at each endpoint

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Sides

The segments that form the polygon

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Vertex

An endpoint of a side of the polygon

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Convex

No line that contains a side of the polygon contains a point in the interior of the polygon

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Concave

A polygon that is not convex

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Equilateral

All sides of the polygon are congruent

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Equiangular

All interior angles of the polygon are congruent

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Regular

Occurs when a polygon is equilateral and equiangular

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Diagonal

A segment that joins two nonconsecutive certified

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Quadrilateral Sum Conjecture

The sum of the measures of the 4 angles of any quadrilateral is 360 degrees

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Pentagon Sum Conjecture

The sum of the measures of the 5 angles of any pentagon is 540 degrees

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Polygon Sum Conjecture

The sun if the measures of the n-interior angles of an n-gon is 180(n-2)

  • To find the measures of the interior angles we use 180(n-2)/n

  • To find the measures of the exterior angles we use 180-180(n-2)/n

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Parallelogram

Is a quadrilateral with both pairs of opposite sides parallel

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Parallelogram Opposite Angles Conjecture

Opposite angles in a parallelogram are congruent

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Parallelogram Consecutive Angle Conjectures

Adjacent angles in a parallelogram are supplementary

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Parallelogram Opposite Sides Conjectures

Opposite sides of a parallelogram are equal in length

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Parallelogram Diagonals Conjecture

The diagonals of a parallelogram are bisected by the point of their intersection

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Opposite Sides Theorem Converse

If the opposite sides of a quadrilateral are congruent, then the figure is a parallelogram

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Opposite Angles Theorem Converde

If the opposite angles of a quadrilateral are congruent, then the figure is a parallelogram

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Consecutive Angles Theorem Converse

If the consecutive angles of a quadrilateral are supplementary, then the figure is a parallelogram

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Diagonals Theorem Converse

If two diagonals of a quadrilateral bisect each other, then the figure is a parallelogram

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Rhombus

A parallelogram with 4 congruent sides

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Rectangle

A parallelogram with 4 right angles

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Square

A parallelogram with 4 congruent sides and 4 right angles

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Rhombus Diagonals Conjecture

The diagonals of a rhombus are perpendicular and they bisect each other

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Rhombus Angles Conjecture

The diagonals of a rhombus bisect the angles of a rhombus

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Theorem 6.12 A

A parallelogram is a rhombus if, and only if, it’s diagonals are perpendicular

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Theorem 6.12 B

A parallelogram is a rhombus if, and only if, each diagonal bisects a pair of opposite angles

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Rectangle Diagonals Conjecture

The diagonals of a rectangle are congruent, and bisect each other

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Theorem 6.13 A

A parallelogram is a rectangle if, and only if, it’s diagonals are congruent

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Square Diagonals Conjecture

The diagonals of a square are congruent, perpendicular, and bisect each other

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Trapezoid

A quadrilateral with exactly one pair of parallel sides

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Bases of a Trapezoid

The parallel sides of a trapezoid

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Base Angles of a Trapezoid

A trapezoid has two pairs of base angles. Each pair of base angles shares a side

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Legs of a Trapezoid

The non-parallel sides

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Isosceles Trapezoid

A trapezoid with congruent legs

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Midsegment of a Trapezoid

The segments that connect the midpoints to the legs

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Theorem 6.14

If a trapezoid is isosceles, then each pair of base angles is congruent

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Theorem 6.16

A trapezoid is isosceles if, and only if, it’s diagonals are congruent

  • The consecutive angles between the bases of a trapezoid are supplementary

  • The mid-segment of a trapezoid is parallel to each base and its length is ½ the sun of the length of the bases

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Kite

A quadrilateral that has two pairs of consecutive congruent sides, but it’s opposite are not congruent

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Vertex Angles

The two angles between each pair of congruent sides

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Kite Angles Conjecture

Non-vertex angles are congruent

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Kite Diagonals Conjecture

Diagonals of a kite are perpendicular

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Kite Diagonals Bisector Conjecture

The diagonals connected the vertex angles of a kite is the perpendicular bisector of the other diagonal

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Kite Angle Bisector Conjecture

The vertex angles of a kite are bisected by a diagonal