Geometry Final Study Guide – Flashcards
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Triangle congruence
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SSS, SAS, ASA, AAS, and HL
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Segment Addition Postulate
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AC + AB= AB
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Angle Addition Postulate
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If P is the interior of RST, then m RSP + m PST=m RST
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Linear Pairs
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any two angles that form a line (adjacent)
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Complementary Angles
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two angles that add to be 90 degrees
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Supplementary Angles
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two angles that add to be 180 degrees
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Vertical Angles
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opposite angles that are congruent
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Original
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If m A=30 , then A is acute
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Inverse
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If m A=30 , then A is not acute
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Converse
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If A is acute, then m A=30
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Contrapositive
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If A is not acute, then m A=30
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Point, Line, and Plane Postulates
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-Through any two points there exists exactly one line -A line contains at least two points -If two lines intersect, then their intersection is exactly one point -Through any three noncollinear points there exists exactly one plane -A plane contains at least three noncollinear points -If two points lie in a plane, then the line containing them lies in the plane -If two planes intersect, then their intersection is a line
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Law of Detachment
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If p>q is a true conditional statement and p is true, then q is true
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Law of Syllogism
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If p>q and q>r are ture conditional statements, then p>r is true
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Reflexive
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For any real number, a=a
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Symmetric
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If a =b, then b = a
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Transitive
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If a = b and b = c, then a = c
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Substitution
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If a = b, then a can be substituted for b in any equation or expression
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Slope
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m = rise/run y2-y1/x2-x1 y=mx+b perpendicular- opposite (3/5 and -5/3) parallel- same slope and different y-intercept
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CA
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Correspond in position
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AIA
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Alternate Interior Angles
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AEA
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Alternate Exterior Angles
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SSIA
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Same Side Interior Angles
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CAP
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If two parallel lines are cut by a transversal, then the corresponding angles are congruent
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CAP converse
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If two lines are cut by a transversal so that corresponding angles are congruent, then the two lines are parallel
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Exterior Angle Theorem
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the measure of the exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
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Triangle Sum Theorem
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mangle 1 + mangle 2 + mangle 3 = 180 degrees (interior angle)
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Perpendicular Bisector
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the point of concurrency is called the circumcenter
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Angle Bisector
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The point of concurrency is called the incenter
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median
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a segment drawn from a vertex of a triangle to the midpoint of the side opposite
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centroid
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the point of concurrency of the medians of a triangle (center of a triangle)
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altitude
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vertex to the opposite side meeting at a right angle (height of an object)
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Hinge Theorem
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if two sides of one triangle are congruent to two sides of another triangle, and the included angles of the first are larger than the included angle of the second, then the third side of the first is larger than the third side of the second.
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heron's Formula
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s= 1/2 (a + b + c) A= s(s-a)(s-b)(s-c)
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Transformation
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is an operation that maps or moves the pre-image onto the image rigid transformation= reflection, translation, rotation
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Isometry
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is a type of transformation that preserves shape, size, length, and area
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Reflection
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Properties: opposite orientation, same size and shape, distance to the reflection line is the same, and draw from a point to another point has to meet the reflection at a 90 degree angle
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Trapezoid Midsegment
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1/2 (base 1 + base 2)
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Polygons
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1. three or more sides 2. closed figure 3. line segments 4. no extra parts
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Naming Conventions
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triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, n-gon
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Properties of Parallelograms
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1. opposite sides are parallel 2. opposite sides are congruent 3. opposite angles are congruent 4. consecutive angles are 180 degrees 5. diagonals bisect each other
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Angle Sum of Polygons
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increase by 180 degrees [each angle= total angle sum divided by how many sides on shape]
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Square Properties
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1. All properties of a parallelogram 2. all sides are congruent 3. all angles are 90 degrees, they are congruent 4. diagonals create four right angles 5. diagonals are congruent 6. diagonals bisect the angles
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Rectangle Properties
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1. all the properties of a parallelogram 2. all angles are congruent and equal 90 degrees 3. diagonals are congruent
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Rhombus Properties
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1. all properties of a parallelogram 2. all sides are congruent 3. diagonals create four right angles 4. diagonals bisect the angles
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Yes and Nos
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Square can be a rhombus, but a rhombus can't be a square Rhombus can't be a rectangle and a rectangle can't be a rhombus Square can be a rectangle, but a rectangle can't be a square
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image
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doesn't change (x,y) > (x-2, y+1) for (2,-1)
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preimage
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changes
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Translation
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moves an object along a vector, slide or glide {vector-tells direcion and magnitude(size)}
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Rotation
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a transformation in which an object is turned about a fixed point or center of rotation
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Glide Reflection
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1. translation 2. relfection y=x
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Classes of Frieze Patterns
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1. T -translation- 2. TR -translation, rotation- 3. TG -translation, glide reflection- 4. TV -translation, vertical reflection 5. THG -translation, horizontal reflection, glide- 6. TRVG -translation, rotation, vertical reflection, glide 7. TRHVG -translation, rotation, horizontal reflection, vertical reflection, glide
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geometric mean
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a/x = x/b if a and b are equivalent then that equals your x value
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Proportions and ratios
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a/b =c/d, then a/c =b/d A/B = C/D, then A+B/B = C+D/D is equivalent to A/B + A/B = C/D + C/D
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Scale factor
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new/original [no negatives, no zeros]
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dialation
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a transformation that maps or moves an object but changes its size by a scale factor (k) [Reduction shrinks the object and Enlargement enlarges the object]
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Chord
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a segment whos endpoints are on the circle
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Secant
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is a line that intersects a circle in two points and passes all the way through
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Tangent
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is a line that intersects a circle at exactly one point
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Arcs and Chords
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minor arc- less than 180 degrees major arc- greater than 180 degrees semicircle- 180 degrees
