Geometry Final Exam Study Guide – Flashcards
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corresponding angles
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2 non-adjacent angles on the same side of the transversal with one interior and one exterior
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transversal
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a line which cuts across two other lines that may or may not be parallel
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parallel lines
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Lines that do not intersect and are not skew. Slopes of parallel lines are the same in value and sign.
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interior
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the space between parallel lines
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exterior
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the space above and below parallel lines
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Same-Side Interior Angles (SSIA)
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2 interior angles on the same side of the transversal
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Alternate Interior Angles (AIA)
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2 nonadjacent interior angles on the opposite sides of a transversal
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Alternate Exterior Angles (AExA)
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ask
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Corresponding Angles Postulate (C.A.P.)
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If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
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Alternate Interior Angles Theorem
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If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
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Same-Side Interior Angles Theorem
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If 2 parallel lines are cut by a transversal, then the pairs of same-side interior angles are congruent.
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Vertical Angles
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Opposite angles when two lines cross
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Vertical Angle Theorem (VAT)
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If two angles are vertical angles, then they are congruent.
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Converse of AIA Theorem
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If a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, then the two lines are parallel.
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Converse of SSIA Theorem
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If a transversal intersects two lines in such a way that a pair of same-side interior angles are supplementary, then the two lines are parallel.
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Converse of CAP
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If a transversal intersects two lines in such a way that a pair of corresponding angles are equal, then the two lines are parallel.
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Transitive Property
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If a=b and b=c, then a=c.
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Reflexive Property
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a=a
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Symmetric Property
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If a=b, then b=a.
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similar polygons
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polygons whose vertices can be paired in such a way that corresponding angles are congruent and corresponding sides are proportional
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scale factor
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the ratio of the lengths of corresponding sides of similar polygons
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reduction
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The copy is smaller than the original figure
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enlargement
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The copy is larger than the original figure
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proportional
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corresponding in size or amount to something else
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corresponding parts
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the angles, sides, and vertices that appear in the same places in two similar or congruent figures
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ratio of perimeter
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If 2 polygons are similar with a scale factor of a:b, then the ratio of their perimeters is a:b.
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ratio of areas
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If 2 polygons are similar with a scale factor of a:b, then the ratio of their areas is a²:b².
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similarity statement
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a statement stating similarity between two figures
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original figure
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first figure
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copy
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second image that is similar to original
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prime notation
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using prime symbols ( ' ) to show how many copies of similar figures
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SSS~
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If all 3 corresponding sides in a triangle are proportional, then the triangles are similar.
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SAS~
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If 1 angle in the original triangle is congruent to another angle in the copy image, and the sides, in each figure, which make the angle inclusive are in proportion, then the two triangles are similar.
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AA~
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If 2 angles in the original triangle are congruent to two angles in a copy, then the two triangles are similar.
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Area of a Parallelogram
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A= b₁h₁
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Altitude
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a segment that starts at an angle/vertex and is perpendicular to its receiving side *each base goes with its own altitude
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parallelogram
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a quadrilateral with 2 pairs of opposite, congruent sides that are parallel
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Perimeter
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a linear measurement of the sum of the lengths of a shape's sides
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area
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a squared measurement of the number of non-overlapping square units contained in the interior of a figure
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Height
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the length of any altitude
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Base
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the side to which an altitude is drawn
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Area of a Triangle
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The area of a triangle equals half of the product of the base and the hight to that base, or A=½bh.
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Area of a Rhombus
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The are of a rhombus equals half the product of the lengths of its diagonals, d₁ and d₂, or A=½d₁d₂
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Area of a Square
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The area of a square is the square of the length of one side, s, or A=s².
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Area of A Congruence Postulate
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If 2 polygons are congruent, then they have the same area.
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Area Addition Postulate
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The are of a region is the sum of the area of all its non-overlapping parts.
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Area of a Trapezoid
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A=½h (b₁+b₂) ---- b₁ and b₂ are parallel sides
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Area of Rectangle
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A= bh
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Area of Regular Polygons
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A= (½)(apothem)(perimeter)
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Circumference of a Circle
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C=2πr
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Area of a Circle
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A= πr²
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Linear Measurement
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1-dimension (ex. ft, cm, in, ect.)---- for perimeter
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Squared Measurement
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2-dimensions (ex. ft², cm², in², ect.) ---- for area
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Pythagorean Triples
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3 integers that fit the pythagorean theorem
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regular polygon
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equiangular and equilateral
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square root
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√
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radical
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a root of a number or quantity
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radicand
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the number inside the root
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index
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the nth root
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rationalized denominator
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multiplying an irrational 1 so that the irrational denominator of a fraction becomes rational
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30-60-90 triangle
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short leg- 1 unit long leg- √3 units hypotenuse- 2 units
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45-45-90 triangle
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legs are congruent- 1 unit ea. hypotenuse- √2 units
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hypotenuse
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side across from the largest angle
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Pythagorean Theorem
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A²+B²=C²
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Converse of the Pythagorean Theorem
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If A, B, and C are the lengths of a triangle such that A²+B²=C², then the triangle is a right triangle.
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apothem
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starts at center of regular polygon and ends at the midpoint of a side
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radius
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starts at the center and ends at a vertex of the regular polygon
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prism
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3D figure with 2 bases and 3+ faces
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lateral edge
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a segment that is the intersection of two lateral faces
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right prism
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prism in which the lateral edges are perpendicular to the bases
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oblique prism
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a prism that is not a right prism
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regular prism
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the lateral faces of a prism are all congruent rectangles and both bases are regular polygons
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pyramid
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a 3D figure that the lateral faces connect to one common vertex, only 1 base
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right pyramid
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a pyramid whose base has rotation symmetry and the segment from the vertex to the center of symmetry is perpendicular to the base
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regular pyramid
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a right pyramid whose base is a regular polygonal region
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lateral area
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the combines are of all of the faces (no bases)
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surface area
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combined area of all bases and faces
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Volume
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the amount of space that a substance or object occupies, or that is enclosed within a container
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LA of prisms and cylinders
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LA= (perimeter of base)(height)
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SA of prisms and cylinders
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SA= LA+ 2(area of base)
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LA of pyramids and cones
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LA= ½(perimeter of base)(slant height)
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SA of pyramids and cones
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SA= LA+ (area of base)
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Volume of prisms and cylinders
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V= (base)(h)
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Volume of pyramids and cones
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V= 1/3(base)(h)
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Sine
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sinθ= opp/hypot
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Cosine
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cosθ= adj/hypot
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Tangent
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tanθ= opp/adj
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Inverse of Sine
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sin⁻¹(x)= θ
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Inverse of Cosine
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cos⁻¹(x)= θ
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Inverse of Tangent
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tan⁻¹(x)= θ
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Angles of Elevation
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angles above the horizontal, like looking up from ground level toward the top of a flagpole.
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Angles of Depression
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Angles of depression or declination are angles below the horizontal, like looking down from your window to the base of the building in the next lot.
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parallelogram
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a quadrilateral with 2 pairs of opposite, congruent sides that are parallel -2 pairs of opp. sides are parallel -2 pairs of opposite sides are congruent -opposite angles are congruent -diags bisect ea. other
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square
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a quadrilateral with two pairs of opposite sides that are parallel and is both equiangular and equilateral -2 pairs of opp. sides are parallel -2 pairs of opposite sides are congruent -all sides are congruent -opposite angles are congruent -all angles are right angles -diags bisect ea. other -diags are congruent -diags are perpendicular -diags bisect opposite angles
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rhombus
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a quadrilateral with two pairs of opposite sides that are parallel that is equilateral, but not equiangular -2 pairs of opp. sides are parallel -2 pairs of opposite sides are congruent -all sides are congruent -opposite angles are congruent -diags bisect ea. other -diags are perpendicular -diags bisect opposite angles
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rectangle
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a quadrilateral with two pairs of opposite sides that are parallel and is equiangular, but not equilateral -2 pairs of opp. sides are parallel -2 pairs of opposite sides are congruent -opposite angles are congruent -all angles are right angles -diags bisect ea. other -diags are congruent
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quadrilateral
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a polygon with 4 sides
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kite
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a quadrilateral figure having two pairs of equal adjacent sides, symmetrical only about its diagonals. (no parallel sides)
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trapezoid
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a quadrilateral with one pair of opposite sides that are parallel -2 bases are parallel
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Properties of Isosceles Trapezoid
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1. one pair of opposite sides (bases) are parallel 2. 2 congruent legs 3. 2 pairs of congruent base angles 4. Diagonals are congruent
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5 Ways to Prove a Parallelogram
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1. Two pairs of pairs of opposite sides are parallel. 2. Two pairs of pairs of opposite sides are congruent. 3. One pair of opposite sides is both parallel and congruent. 4. Two pairs of opposite congruent angles. 5. Two diagonals that bisect each other.
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Properties of a Kite
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1. Diagonals are perpendicular to each other. 2. The long diagonal bisects the short diagonal, but not vice versa. 3. Only the long diagonal bisects its receiving angles. (angles are not congruent) 4. The short diagonal does not bisect its receiving angles, but those two angles are congruent.
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midsegment
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midseg= (b₁+b₂)/2
