Common Core Geometry Regents Review Flashcards | Quizlet

Common Core Geometry Regents Review

Tangent
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Terms in this set (92)
Tangent
intersects a circle in only 1 place.
Image: Tangent
Secant
intersects a circle in 2 places.
Image: Secant
Intersection of a tangent and a radius
form right angles when they intersect.
Image: Intersection of a tangent and a radius
Equation of a circle
x minus h squared plus y minus k squared equals radius squared.
Image: Equation of a circle
Circumference of a circle
2 times pi times radius or pi times diameter.
Image: Circumference of a circle
Area of a circle
pi times radius squared.
Image: Area of a circle
Central angle
is equal to its intercepted arc.
Image: Central angle
Inscribed angle
is equal to ½ its intercepted arc.
Image: Inscribed angle
Angle formed by 2 chords intersecting in a circle
is equal to the sum of the arcs divided by 2.
Image: Angle formed by 2 chords intersecting in a circle
Angle formed by 2 secants
is equal to the major arc minus the minor arc divided by 2.
Image: Angle formed by 2 secants
Angle formed by a secant and a tangentis equal to the major arc minus the minor arc divided by 2.Angle formed by two tangentsis equal to the major arc minus the minor arc divided by 2.Lengths of 2 intersecting chordspart of the first chord times the other part of the first chord equals a part of the second chord times the other part of the second chord.Lengths of an intersecting diameter and chord that meet at right angles (perpendicular)if a diameter meets a chord at a right angle (perpendicular), the diameter divides the chord into 2 equal parts. (POP=POP)Lengths of 2 intersecting secantsthe whole length of the first secant times the outside length of the first secant equals the whole length of the second secant times the outside length of the second secant. (WO=WO)Lengths of an instersecting secant and tangentthe whole length of the first secant times the outside length of the first secant equals the length of the tangent squared. (T^2 = WO)Lengths of intersecting tangentsTangents to a circle sharing a common vertex are equal. (Party Hat)Anglesacute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles are between 90 and 180 degrees. Straight angles are 180 degrees and reflex angles are greater than 180 degrees.Adjacent anglesshare a common vertex, a common side, but not common interior points.Complementary angles2 angles when added together that equal 90 degrees. They do not have to be adjacent angles.Supplementary angles2 angles when added together that equal 180 degrees.They do not have to be adjacent angles.Vertical anglesvertical angles are congruent.Alternate interior anglesalternate interior angles are congruent.Corresponding anglescorresponding angles are congruent.Sum of the angles in a trianglethe 3 angles of a triangle add up to 180 degrees.Triangles classified by sidesscalene triangles have no equal sides. isosceles triangles have at least 2 equal sides. equilateral triangles have 3 equal sides.Triangles classified by anglesacute triangles have 3 acute angles. right triangles have a 90 degree and 2 acute angles. obtuse triangles have an obtuse and 2 acute angles.Exterior angle of a trianglethe exterior angle of a triangle equals the sum of the 2 opposite interior angles.Isosceles trianglessides opposite congruent angles are congruent. angles opposite congruent sides are congruent.Mid segment of a trianglea mid segment connects the midpoint of 2 sides of a triangle and is equal to ½ the side not containing the 2 midpoints.Medianbisects the opposite side into 2 congruent line segments. they meet in a triangle at a point called the centroid. median segments are in a ratio of 2 to 1.Angle bisectorbisects an angle into 2 congruent angles. they meet in a triangle at a point called the incenter.Altitudemakes a right angle with the opposite side. they meet in a triangle at a point called the orthocenter.Perpendicular bisectorbisects and makes a right angle with a side of a triangle.They meet in a triangle at a point called the circumcenter.Similar trianglesangles in similar (∼) triangles are congruent. sides are in proportion. angles are in a proportion of one to one. (1:1)Proving triangles similarneed only 2 angles to be congruent to probe 2 triangles similar.Proving triangles congruentcan not be angle angle side (A.S.S.) or side side angle(S.S.A.).C.P.C.T.C.corresponding parts of congruent triangles are congruent.Pythagorean theorema squared plus b squared equals c squared. the hypotenuse is always c.Proving right triangles congruenthypotenuse leg.Right triangle ratios(HLLS or SAAS)Slopefrom left to right. up the hill is positive slope. down the hill is negative slope. a horizontal line has 0 slope and a verical line as an undefined slope.Point slope form of a liney minus y one equals slope (m) times x minus x one.Slope intercept form of a liney equals slope (m) times x plus the y intercept (b)Slope formulay two minus y one divided by x two minus x one. rise over run.Distance formulathe square root of x two minus x one squared plus y two minus y one squared.Midpoint formulax one plus x two divided by two is the x coordinate. y one plus y two divided by two is the y coordinate.Find the endpoint of a line given the midpoint and the other endpointthe integers added to the coordinates of C to get the coordinates of M are added to the coordinates of M to get the coordinates of D.Finding the slope and y intercept of a liney must be positive and isolated on one side of the equation.Slopes of parallel lineshave the same slope and a different y intercept.Slopes of perpendicular linesthe slopes are negative reciprocals. to find the negative reciprocal make the slope a fraction, flip it, and change the sign.Surface area of a rectangular prism2 times the sum of the length times the width, the length times the height. and the width times the height.Volume of a rectangular prismlength times width times height.Polygonsa triangle has 3 sides. a quadrilateral has 4 sides. a pentagon has 5 sides. a hexagon has 6 sides. a octagon has 8 sides. a decagon has 10 sides.Perimeterdistance around the outside of a polygon.Parallelogramsopposite sides are parallel. opposite sides and angles are congruent. consecutive angles are supplemental (add to 180). diagonals bisect each other.Rectangleopposite sides are parallel. opposite sides are congruent. contains 4 right angles. diagonals are congruent and bisect each other.Squareopposite sides are parallel. all sides are congruent and meet at right angles. diagonals are congruent and perpendicular(make right angles). diagonals bisect each other and the angles of the square.Rhombusopposite sides are parallel. all sides are congruent. diagonals are congruent and perpendicular(make right angles). diagonals bisect each other and the angles of the rhombus.Trapezoidone set of parallel sides.Median of a trapezoidthe top parallel side plus the other parallel side divided by 2.Isosceles trapezoidone set of parallel sides. non-parallel sides are congruent. base angles are congruent. diagonals are congruent.Area of a trapezoid½ times the height times the sum of the 2 parallel sides.Transformationsdilations are a capital D. reflections are a lower case r. rotations are a captital R. translations are a capital T.Dilationmultiply the coordinate by the scale factor.Reflection over the x axischange the sign of the y coordinate.Reflection over the y axischange the sign of the x coordinate.Reflection over the line y=xswitch the x and y coordinates.Rotation of 90 degreesgraph the coordinate. rotate the graph 90 degrees counter clockwise and read the new point.Rotation of 180 degreesgraph the coordinate. rotate the graph 180 degrees counter clockwise and read the point.Rotation of 270 degreesgraph the coordinate. rotate the graph 270 degrees counter clockwise and read the point.Translationadd the 2 integers to the orginal coordinate. add the first integer to the x coordinate and the second integer to the y coordinate.Glide reflectiona refection combined with a translation.Collinear pointsare points that lie on the same lineSkew Linesare lines on different planes that never touch.CentroidPoint where the MEDIANS of a triangle are concurrent. The centroid divides a the median into a 2:1 ratio.Linear Pairs are _____________________.supplementaryRigid MotionsReflection, Rotation and Translation. These transformations preserve the size and shape of the object.Given parallel lines, name two types of congruent angles to look for.Alternate Interior angles are congruent. Corresponding angles are congruent.I am a parallelogram with perpendicular diagonals, who am I?RhombusI am a parallelogram with congruent diagonals, who am I?RectangleEquation of a vertical linex = a Vertical lines have no slope.Equation of a horizontal liney = b Horizontal lines have equal to 0.Arc length(degree/360)*pi*diameter "a fraction of the total circumference"Area of a sector(degree/360)*pi*r^2 "a fraction of the total area"Triangle Inscribed into a semicircleMust be a right angle/triangleConvert from degrees to radiansmultiply by pi/180 (on formula sheet)Convert from radians to degreesmultiply by 180/pi (on formula sheet)What formula should you use to find length or show segments are congruent?distance formulaWhat formula should you use to show lines parallel or perpendicular?slope formulaWhat formula should you use to show segments bisect each other?midpoint formuladensitymass/volume