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Geometry 2nd Semester Exam Vocabulary
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Gravity
Terms in this set (64)
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Converse of Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector
Angle Bisector Theorem
If a point lies on the bisector of an angle, then it is equidistant from the sides of the angle
Converse of Angle Bisector Theorem
If the point is in the interior of an angle and equidistant from the sides, then it is on the angle bisector
Circumcenter Theorem
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the veritces
circumcenter
point of concurrency of the perpendicular bisectors
median
segment that has endpoints on a vertex and the opposite midpoint in a triangle
inncenter
point of concurrency of the angle bisectors
centroid
point of concurrency of the medians
Centroid Theorem
The centroid lies 2/3 the way along the median from the vertex to the mdpt of the opposite side
Triangle Sum Theorem
Interior Angles of a Triangle add to 180 degrees
Polygon Interior Angle Sum Theorem
The sum of the interior angles of any convex n-gon is (n-2)(180)
Corollary to Polygon Angle Sum Theorem
The measure of the angle of a regular n-gon is (n-2)180/n
Polygon Exterior Angle Sum Theorem
The sum of the exterior angles in a convex n-gon is 360 degrees
Corollary to Polygon Exterior Angle Sum Theorem
The measures of each exterior angle in a regular convex n-gon is 360/n
Properties of Parallelorgram
-Sides are congruent
Opposite Angles are Congruent
-Consecutive Angles are Supplementary
-Diagonals Bisect each other
Properties of Rhombus
-Equilateral
-All sides are Congruent
-Diagonals are angle bisectors and perpendicular
Properties of Square
-Diagonals are Congruent
-Opposite Sides are Parallel
-Opposite Angles Congruent and Supplementary
- Equilangular
-Opposite sides are congruent
-Equilateral
-All sides are Congruent
-Diagonals are angle bisectors and perpendicular
Properties of Rectangle
-Diagonals are Congruent
-Opposite Sides are Parallel
-Opposite Angles Congruent and Supplementary
- Equilangular
-Opposite sides are congruent
Properties of Kite
-Diagonals are Angle Bisectors and Perpendicular
-2 pairs of congruent sides
-1 pair of congruent angles
Properties of Isosceles Trapezoid
-Legs and Base Angles are congruent
-Diagonals are congruent
-Opposite Sides are Parallel
Definition of Similar
Angles are all congruent and all sides are proportional
Ways to Prove Triangles are Similar
AA similarity, SAS similarity, or SSS similarity
AA Similarity
SSS Similarity
SAS Similarity
Side Splitter Theorem
If a line cuts a triangle parallel to one of it's sides, then it cuts the sides porportionally
Corollary to Side Splitter Theorem
If three (or more) lines are cut by 2 traversals, then they are cut proportionally
Triangle Bisector Theorm
If a ray bisects an angle in a triangle, then it cuts the opposite side proportionally to the other two sides
Pythagorean Triple
Satisfy the Pythagorean theorem and are all natural numbers
Obtuse Triangle
c^2>a^2+b^2
Right Triangle
c^2=a^2+b^2
Acute Triangle
c^2<a^2+b^2
Angle of Depression
Angle down from a horizontal
Angle of Elevation
Angle up from a horizontal
sin
o/h
cos
a/h
tan
o/a
Transformation
Operations that move a pre image onto an image
Reflection
Mapping of a point over a line; both points are equidistant and perpendicular to that line
Translation
A transformation that maps all points of a figure to a new figure the same distance and the same direction
Dialation
Transformation that causes the image to shrink or enlarge in proportion to the original size
Rotation
A turn about a fixed point. Write it with the center, direction, and angle measure
Glide Reflection
A composition of a translation and a reflection such that the translation is parallel to the line of reflection (order does not matter)
Rotational Symmetry
The figure can be mapped onto itself by a rotation of 180 degrees or less
Line Symmetry
The figure can be reflected onto itself
Scale Factor
Image/Preimage
Isometry
The figures remain congruent
Tangent Line
Touches a circle at one point
Secant Line
Touches a circle at two points
Chord
segment with endpoints on the circle
Central Angle
angle where the vertex is the center of the angle
Inscribed Angle
angle where vertex is on the circle
Intercepted Arc
Part of the circle that the rays of an angle tough
Tangent Line Theorem
A tangent line to a circle is always perpendicular to the radius
Chord and Arc Theorems
Within a circle or two congruent circles,
-congruent central angles have congruent intercepted arcs
-congruent central angles have congruent chords
-congruent chords have congruent arcs
-chords equidistant from the center are congruent
If a diameter is perpendicular to a chord, then it bisects the chord and its intercepted arc
If a diameter bisects a chord, then it is perpendicular to the chord
The perpendicular bisector of a chord contains the center of the circle, it is the diameter
Inscribed Angle Theorem
The measure of an inscribed angle is always 1/2 the measure of it's intercepted arc
Corollaries of Inscribed Angle Theorem
If two inscribed angles intercept the same mark, then they are congruent
Any angle inscribed in a semi circle is right
If a quadrilateral is inscribed in a circle. then it's opposite angles are supplementary
The measure of an angle formed by a tangent and a chord is 1/2 the measure of the intercepted arc
Angle Measures Theorems
If you have 2 chords that intersect inside a circle, the measure of the angle is 1/2 the sum of the intercepted arcs
If you have 2 chords that intersect outside a circle, the measure of the angle is 1/2 the difference of the intercepted arcs
Power Point Theorem
For a given point and a given circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and the circle
Standard Form Equation of a Circle
r^2=(x-h)^2+(y-k)^2
Circle
The set of all points that are equidistant from a given point (center)
Enlargement
Scale factor greater than 1
Reduction
Scale factor less than 1 and greater than 0
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