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Geometry Regents Review
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Terms in this set (92)
Unit One: Basic Geometry/Constructions
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Equilateral Triangle
All sides are congruent
Isosceles Triangle
2 of the sides are congruent
Angle Bisector
Line that cuts an angle in half
Altitude
Line that starts at an angle and extends to the opposite segment which then forms a right angle
Perpendicular Lines
Two lines that meet and form a right angle
Col-linear Points
Three points that lie on the same line
Scale Triangle
Zero sides are congruent
Perpendicular Bisector
Line that forms the midpoint of a segment and forms a right angle
Median
Line segment joining a vertex to the midpoint of an opposite side
Unit Two: Unknown Angles
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Vertical Angles
Pairs of opposite angles made by two intersecting lines
Linear Pairs
Adjacent angles formed by two intersecting lines
Complementary Angles
Two angles who's sum is 90 degrees
Supplementary Angles
Two angles who's sum is 180 degrees
Alternate Interior Angles
When two lines are cut by a transversal, alternate interior angles are formed and made congruent
Corresponding Angles
The angles that are at the same relative position at each intersection where a transversal cuts through them and if the two lines are parallel than the corresponding angles are congruent
Same Side Interior Angles
When 2 parallel lines are cut by a transversal, than the same side interior angles are supplementary
Same Side Exterior Angle
When 2 parallel lines are cut by a transversal, than the same side exterior angles are supplementary
Remote Interior Angle Theorem
When an exterior angle is formed the remote interior angles are just two angles that are inside the triangle and opposite the exterior angle.
Auxilary Line
Extra line needed to complete a proof in plane geometry
Unit 5: SSS, SAS, ASA
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Congruent Triangles
When all three sides in one triangle are equal to the corresponding sides in the second triangle
SAS
If two pairs of sides of two triangles are equal in length and the included angles are the same measure than the triangles are congruent
SSS
When three pairs of sides of two triangles are equal in length, then the triangles are congruent
ASA
When two angles and the included side of one triangle are equal to two angles and the included side in another angle, then the triangles are congruent.
Unit 6: AAS, HL, Overlapping Triangle
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AAS
Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles
Isosceles Triangle Theorom
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of the Isosceles Triangle Theorom
If two angles of a triangle are congruent , then the sides opposite to these angles are congruent.
Hyp-Leg
If any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles
Unit 7: Parallegrams
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Properties of a Parallelogram
Opposite sides are congruent, Opposite angels are congruent, Consecutive angles are supplementary, If one angle is right, then all angles are right, The diagonals of a parallelogram bisect each other.
Unit 8: Rectangle, Rhombus and Squares
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Properties of a Rectangle
All the properties of a parallelogram apply, All angles are right angles, The diagonals are congruent.
Properties of a Rhombus
All the properties of a parallelogram, All sides are congruent, The diagonals bisect the angles.
Properties of a square
The diagonals bisect each other and are 90°, The diagonals bisect its angles., Opposite sides are both parallel and equal in length, All four angles are equal, All four sides are equal, The diagonals are equal.
Unit 9: Equation of Lines
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Slope Formula
(y2-y1) + (X2-X1)
Midpoint Formula
(X1+X2/2, Y1+Y2/2)
Slope Intercept Form
y=1/2mx+b
Vertical Line Equation
x=b (Some number)
Horizontal Line Equations
y=b
Point Slope Formula
(y-y1)=(x-x1)
Equations for parallel lines
Same slope but different y-intercept
Equations for perpendicular lines
Negative reciprocals
Writing the equation of the median
Use the point form of a line equation and the midpoint
Writing the equation of an altitude
You need a point (x,y) and the gradient of the opposite side. Find the equation of the median through the other angle
Writing the equation of a perpendicular bisector
All you need to do is find the midpoint and negative reciprocal of the other line and put it into slope intercept form
Unit 10: Coordiante Geometry
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Distance Formula
The square root of (x2-x1)squared + (y2-y1)squared
Proving an isosceles triangle
Prove 2 sides are congruent
Proving and equilateral triangle
prove that all of the sides are equal
Proving a scalene triangle
prove that no sides are congruent
Proving a right angle
prove that there is a 90 degree angle
Proving a parallelogram
Prove that the 2 pairs of opposite sides are parallel
Proving a rectangle
Opposite sides are congruent and parallel, also the alternate interior angles are congruent
Proving a rhombus
If the diagonals bisect all the angles, then it's a rhombus
Proving a square
prove all 4 sides are congruent and parallel
Unit 11: Basic Trig
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Sine
side opposite the given angle and hypotenuse
Cosine
side adjacent the given angle and hypotenuse
Tangent
side opposite the given and adjacent angle
Relationship between sine and cosine
The cosine of any acute angle is equal to the sine of its complementary
Unit 13: Transformations
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Reflection
Ridged motion where image is flipped over the y-axis or x-axis
Rotation
Motion on a graph where you preserve one point
Dilation
Ridged motion where image decreases in size but stays the same shape
Unit 14: similar triangles and proportions
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Angle bisector theorem
Bisector that divides the opposite side into 2 equal segments congruent to the other 2 segements
Altitude rule
Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse
Leg rule
The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
Section Formula
It tells you the points that divides a segment into two pieces
Unit 17: Circles
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Radius
Line segment from a center to any point in the circle
Cord
segment whose endpoints are points on the circle
Diameter
chord passing through the center of a circle
Secant
line starting from an exterior point intersecting the circle in 2 point
Tangent
line starting from an exterior point intersecting the circle at one point
Arc
any connected part of a circle
Minor arc
arcs measuring less than 180
Major arc
arcs measuring more than 180
Semi-circle
half a circles which measures 180
Central angle
angle whose vertex is in the center of the circle
Inscribed angle
angle whose vertex is on the circle and whose sides contain chords of the circle
Angle inscribed in a semi circle
Vertex is on the edge the semi vertex
Floating angles
an angle formed by 2 chords intersecting within a circle
Tangent radius
Radius constructed from a tangent
Common tangent
a line that is tangent to each of the two circles
Tangent chord angle
angle chord formed by a tangent and chord
Tangent tangent angle
angle tangent formed by a tangent and tangent
Secant secant angle
angle secant formed by a secant and a secant
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