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Geometry Regents Review
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Gravity
Terms in this set (100)
(3,4,5) (5,12,13) (8,15,17) (7,24,25)
Name 3 Pythagorean triples
Where the perpendicular bisectors intersect
What is the circumcenter of a triangle?
Where the angle bisectors intersect
What is the incenter of a triangle?
Where the altitudes intersect
What is the orthocenter of a triangle?
Where the medians intersect
What is the centroid of a triangle?
two equal sides and two equal angles
Define isosceles triangle.
a triangle with no congruent sides
Define scalene triangle.
A triangle with three congruent sides
equilateral triangle
a polygon with all sides and all angles equal
Define regular polygon
A polygon with 5 sides
Define pentagon
A polygon with 6 sides
Define hexagon
A polygon with 7 sides
Define septagon/heptagon
A polygon with 8 sides
Define octagon
a polygon with 9 sides
Define nonagon
A polygon with 10 sides
Define decagon
12 sided polygon
Define dodecagon
The height of a triangle (always perpendicular to the base)
Define altitude of a triangle
a segment from a vertex to the midpoint of the opposite side.
Define median of a triangle
a line segment that connects the midpoints of two sides of a triangle
Define midsegment of a triangle
a segment that connects the midpoints of the legs of a trapezoid
Define midsegment of a trapezoid
a trapezoid whose nonparallel opposite sides are congruent
Define isosceles trapezoid
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
What is the Isosceles Triangle Theorem?
A transformation that preserves distance and angle measures
Define rigid motion.
a region inside a circle bounded by two radii of the circle and their intercepted arc; like a slice of pizza
What is a sector of a circle?
an angle whose vertex is the center of the circle; equal to intercepted arc
Define central angle of a circle
an angle whose vertex is on the circle; half of intercepted arc
Define inscribed angle
A quadrilateral with two pairs of parallel sides
Define parallelogram
A parallelogram with four congruent sides
Define rhombus
a parallelogram with four right angles
Define rectangle
A parallelogram with four congruent sides and four right angles.
Define square
The sum of the two nonadjacent interior angles is equal to the exterior angle.
What is the Exterior Angle Theorem?
Vertical (VUX)
Is x=1 horizontal or vertical?
Horizontal (HOY)
Is y=7 horizontal or vertical?
A transformation that preserves angle measure but NOT distance and therefore is not a rigid motion
What is a dilation?
sss, sas, asa, aas, hl
What are the 5 ways to prove triangles are congruent?
aa, sas, sss
What are the 3 ways to prove triangles are similar?
Lines that intersect to form right angles
Define perpendicular lines
lines that never intersect; slopes are equal
Define parallel lines
A bisector divides a segment or angle into two equal parts.
Define bisector
A point that divides a segment into two congruent segments
Define midpoint
(x₁+x₂)/2, (y₁+y₂)/2
What is the midpoint formula?
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
What is the distance formula?
(y₂- y₁) / (x₂- x₁)
What is the slope formula?
y=mx+b
What is the slope intercept form of a line?
y - y1 = m(x - x1)
What is point slope form?
Mass / Volume
What is the density formula?
population/area
What is the population density formula?
Area of a Sector = (central angle/360) x πr²
What is the formula for area of a sector?
Central angle/360 * 2(pi)(r)
What is the formula for arc length?
A pair of opposite congruent angles formed by intersecting lines
What are vertical angles?
Fraction (x2-x1) + x1 [use same formula with y's)
What is the partitioning line segment formula?
First number in ratio/sum of numbers in ratio
How do you make fraction for partition questions?
Pythagorean Theorem (use half of base)
How do you find vertical height if given slant height?
If two prisms or cylinders have the same heights and the same areas for their cross sections, their volumes are equal
What is Cavalieri's Principle?
The sine of an angle is equal to the cosine of its complement
Explain why sin60=cos30
Rigid motions preserve distance and angle measure, keeping the preimage and image congruent
Explain why two figures are congruent after a reflection.
Plot, make a right triangle and do Pythagorean theorem
What is a backup if you forget the distance formula?
(x,y)->(x,-y)
What is the rule for a reflection over x-axis?
(x,y)->(-x,y)
What is the rule for a reflection over y-axis?
(x,y) -> (y,x)
What is the rule for a reflection over y=x?
(x,y)->(-y,-x)
What is the rule for a reflection over y=-x?
Graph it and count boxes!
How do you do a reflection over something like x=2 or y=4?
(x,y) = (-y,x)
What is the rule for a rotation of 90 degrees?
(x,y) = (-x,-y)
What is the rule for a rotation of 180 degrees?
(x,y) -> (y,-x)
What is the rule for a rotation of 270 degrees?
Sliding all the points of a shape according to given directions (up/down, right / left)
Define translation
sinA/a = sinB/b = sinC/c (used to find missing pieces in non-right triangles)
What is the law of sines?
Length
A key word for distance is...
Sum of all the sides
Define perimeter
Draw out all faces, find the area of each and add them up.
How do you find the surface area of a prism?
Line segments whose endpoints are on the circle
Define chord.
Segment that touches the edge of a circle
Define tangent line.
a line that intersects a circle in two points
Define secant line
Congruent
A rectangle has _______________ diagonals.
Perpendicular
A rhombus has _______________ diagonals.
(x-h)^2 + (y-k)^2=r^2
What is the equation for center radius form of a circle?
X squared
Seeing ________ may indicate POSSIBLE factoring
Segment times segment = segment times segment
What is the formula to find a missing length when chords intersect?
Outside times whole = outside times whole
What is the formula to find length when given two secants?
Outside times whole = tangent squared
What is the formula to find length when given one secant and one tangent?
Equal
The slopes of parallel lines are
Negative reciprocals
The slopes of perpendicular lines are
360 divided by the number of sides
How many degrees for a regular polygon to map onto itself by a rotation?
The midpoint (then plug into the equation of a line)
If asked for a perpendicular bisector equation, you need to find the negative reciprocal slope and....
the angle formed by a horizontal line and the line of sight to an object above the horizontal line
Define angle of elevation
The angle formed by a horizontal line and the line of sight to an object below the horizontal line; is located outside the triangle; congruent to the angle of elevation
Define angle of depression
Line reflection
Orientation is not preserved under this transformation
Alternate interior angles
Parallel lines cut by a transversal form these congruent angles that can be identified by a Z shape
Corresponding angles
Parallel lines cut by a transversal form these congruent angles that are in the same location
Any segment or angle is congruent to itself
What is the Reflexive Property?
2 dimensional shape formed when slicing a 3 dimensional shape
What is a cross section?
Cone
Rotating a triangle produces what 3D shape?
Cylinder
Rotating a rectangle produces what 3D shape?
Rhombus and square
These two shapes have diagonals that bisect the angles
Keep the equation the same
When dilating linear equations, if the center of dilation is on the line...
Keep the slope the same (parallelism is preserved under a dilation) but multiply the y-intercept by the scale factor
When dilating linear equations, if the center of dilation is off the line...
You must say the triangles are right triangles before using HL.
What must you add in an HL proof?
The true statement is "All congruent shapes are also similar" because technically they would be in a 1:1 ratio.
Pick the true statement: All congruent shapes are also similar OR all similar shapes are also congruent.
100
How many centimeters are in a meter?
1000
How many meters are in a kilometer? How many grams are in a kilogram?
THIS SET IS OFTEN IN FOLDERS WITH...
Geometry Unit 1 Vocab
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Rigid Motions Practice
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Geometry Unit 2 Vocab
24 terms
Quadrilateral Properties
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