Definitions for Proofs in Math Geometry 24'-25'

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57 Terms

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Congruent Triangles

2 Figures (Triangles) are congruent, if 6 parts of 1 triangle are congruent to 6 parts of another triangle.

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Collinear

Points in or on a straight line.

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Betweenness

A point is between 2 points if and only if the 3 points are collinear.

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Bisects

A point (or segment, ray, or line) that divides a segment into 2 congruent segments.

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Midpoint (and Formula)

The bisection point is called the midpoint of the segment.

Formula: Mx = x1+x2/2 ; y1+y2/2

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Trisection

Trisection points divide segments into 3 congruent segments.

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Angle Bisector

The bisector of an angle is the ray that divides the angle into two congruent angles.

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Angle Trisection

2 lines/rays divide an angle into 3 congruent angles.

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Perpendicularity

If 2 lines/segments are perpendicular, then they form right angles.

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Converse of Perpendicularity

If a right angle has been formed, then it has been formed by perpendicular lines/segments.

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Complementary Angles

2 angles whose sum is 90 degrees.

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Supplementary Angles

2 angles whose sum is 180 degrees.

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Adjacent Angles

Angles next to each other that share a common ray.

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Linear Pair

2 angles that form a straight line.

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Vertical Angles

The angles that are opposite each other.

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Scalene Triangle

A triangle with all sides of different lengths.

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Isosceles Triangle

A triangle with at two sides of equal length.

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Equilateral Triangle

A triangle with all three sides of equal length.

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Equiangular Triangle

A triangle in which all three angles are equal.

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Are equiangular and equilateral triangles reversible?

YES

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Acute Triangle

A triangle where all three angles are less than 90 degrees (all 3 angles are acute in a triangle.)

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Right Triangle

A triangle in which one angle measures exactly 90 degrees (Triangle with only 1 right angle.)

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Obtuse Triangle

A triangle in which one angle measures more than 90 degrees (Triangle with one obtuse angle).

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Perpendicular Bisector

An object (seg, line, ray) that perpendicularly bisects another segment.

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Parallelogram

A parallelogram is a quadrilateral in which

2 pairs of opposite sides are parallel.

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Rhombus

A rhombus is a parallelogram in which at

least 2 consecutive sides are congruent.

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Square

A square is a parallelogram that is both a

rectangle and a rhombus.

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Isosceles Trapezoid

Trapezoid where the not parallel sides are congruent

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Quadrilateral

4 sided figure

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Rectangle

A rectangle is a parallelogram in which at

least 1 angle is a right angle.

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Kite

A kite is a quadrilateral in which 2 dis¬

joint pairs of consecutive sides are con¬

gruent.

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Trapezoid

A trapezoid is a quadrilateral with exactly

1 pair of parallel sides.

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Properties of Parallelogram (5)

  • The opposite sides are parallel by def.

  • The opposite sides are congruent

  • The opposite angles are congruent

  • The diagonals bisect each other

  • Any pair of consecutive angles are supplementrary

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Properties of Rectangle (3)

  • All properties of parallelogram apply by def.

  • All angles are right angles

  • The diagonals are congruent

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Properties of Kite (5)

  • 2 disjoint pairs of consecutive sides are congruent by def.

  • The diagnols are perpendicular

  • 1 diagonal is the perpendicular bisector of the other

  • 1 of the diagonals bisects a pair of opposite sides

  • 1 pair of opposite angles are congruent

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Properties of Rhombus (6)

  • All properties of a parallelogram apply by def.

  • All the properties of a kite apply (half properties become full)

  • All sides are congruent

  • The diagonals bisect the angles

  • The diagonals are perpendicular bisectors of each other

  • The diagonals divide the rhombus into 4 congruent right angles

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Properties of Squares (3)

  • All properties of a rectangle apply by def.

  • All properties of a rhombus apply by def.

  • The diagonals form 4 isosceles right triangles

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Properties of Isosceles Trapezoids (6)

  • The legs are congruent by def.

  • The bases are parallel by def.

  • The lower base angles are congruent

  • The upper base angles are congruent

  • The diagonals are congruent

  • Any lower base angle is supplementary to any upper base angle

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A regular polygon is both _____ and _____.

Equilateral and equiangular

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Ratio

The quotient of 2 numbers

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Proportion

An equation stating that two or more ratios are equal

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Axium…

Postulate

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Similar Polygons are polygons in which:

1) The ratios of the measure of corresponding sides are =

2) Corresponding angles are congruent

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To enlarge =

To make smaller =

Dilation

Reduction

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Dialation

A transformation in which all points of a figure are enlarged or

reduced by a scale factor K, about a center of rotation C such that:

CP′

CP = |K|

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If _____________ then the dilation

is called an ___________________________

• If _____________ then the dilation

is called ______________________________

|K| > 1

Enlargement

|K| < 1

Reduction

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Arc

Arc is made up of 2 pts. on a circle and all the pts. of the circle needed to connect them on a single path.

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Measure

m AB (Arc symbol over AB)

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Length

AB (Arc symbol over AB)

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Sector of a Circle

Portion bounded by 2 radii and an arc of a circle

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Chord

Line segment joining 2 pts. on a circle

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Inscribed Angle

An angle formed by 2 chords

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Prism Def.

A 3-D solid w/ 2 congruent bases and connecting sides

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A rectangular prism has ____ congruent diagnols

4

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