Geometry 454
For Geometry 454-455
Terms
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- Perpendicular
- 2 coplanar lines that intersect to form right angles, ⊥
- corresponding parts
- the sides and angles of 2 triangles that have the same size shape
- midpoint of a segment
- point that divides the segment into 2 congruent segments
- Plane intersection postulate
- 2 planes intersect in a line
- Alternate Exterior angles
- Pairs of non adjacent angles, both exterior, and on opposite sides of the transversal.
- AAS Congruence
- 2 ∠s and the nonincluded side of one triangle are congruent to 2 ∠s and the nonincluded side of another triangle
- diagonal
- a segment that is drawn from one vertex to another and is not one of the sides of a polygon
- Unique plane postulate
- through and 3 non-collinear points there is exactly one plane
- Triangle Sum theorem
- the 3 interior angles of a triangle sum to 180 degrees
- unequal sides theorem
- if 2 sides of a triangle are not congruent, then the angle opposite the longer side is larger than the angle opposite the smaller side
- transversal
- a line that intersects two or more lines
- Unique line postulate
- Through 2 points there is exactly one line
- alternate interior angles
- Pairs of non adjacent angles, both interior, and on opposite sides of the transversal.
- side
- a line bounding a geometric figure
- point
- an exact location in space
- Exterior angle of a triangle
- the measure of an exterior angle of a triangle is equal to the sum of the 2 remote interior angles
- diameter
- line segment that passes through the center of the circle, and whose endpoints lie on the circle
- radius
- line segment whose endpoints are the center of a circle and any point on the circle
- Perpendicular theorem
- if 2 coplanar lines are ⊥ to a third line then they are parallel
- Consecutive vertices
- in a polygon two vertices that are endpoints of the same line
- distance
- absolute value of the difference of their coordinates, between 2 coordinates is √(x₁ - x₂ )² + (y₁ - y₂ )²
- ASA Congruence
- 2 ∠s and the included side of one triangle are congruent to 2 ∠s and the included side of another triangle
- HL Congruence
- if the a leg and the hypotenuse of one right triangle are congruent to the same in another right triangle then the triangles are congruent
- straight angle
- an angle that measures exactly 180°
- congruent
- having the same shape and size, ≅
- perpendicular
- Two lines are perpendicular if they form 4 right angles
- supplementary angles
- two angles whose sums add to 180°
- obtuse triangle
- a triangle with one obtuse angle
- Unequal angles theorem
- if 2 angles of a triangle are not congruent, then the sides opposite the larger of the 2 angles is longer than the side opposite the smaller angle
- equilateral triangle
- a triangle with all congruent sides
- convex polygon
- no diagonal contains a point in outside the polygon
- segment bisector
- A line, segment, or ray that goes through a midpoint of a segment.
- Segment addition postulate
- If point B lies between points A and C on line AC then m of AB + m of BC = m of AC
- kite
- Quadrilateral with 2 pairs of adjacent congruent sides, with perpendicular diagnals
- obtuse angle
- an angle that measures more than 90°
- vertex
- the point where two sides intersect
- remote interior angle
- it is one of the two other angles of the triangle (with which the exterior angle does not form a linear pair)
- right angle
- an angle that measures exactly 90°
- Collinear
- describes a set of points that lie along the same line
- center of a circle
- the point inside a circle that is the same distance from all of the points on the circle
- ray
- part of a line that starts at one endpoint and extends forever
- Same Side Interior angles
- two nonadjacent interior angles that lie on the same side of the transversal.
- Exterior angle Theorem
- In a triangle, the measure of an exterior angle is equal to the sum of the measures of the interior angles at the other two vertices of the triangle - also known as remote interior angles
- Length of a segment
- distance between its endpoints
- line
- a straight path that extends without end in opposite directions
- angle bisector
- a ray dividing a given angle into two congruent angles each half the size of the given angle.
- parts of an isosceles triangle
- the 2 ≅ sides are legs, the non-congruent side is the base, the angles that formed by the base and a leg are base angles, angle formed by the legs is the vertex angle
- Pythagorean theorem
- States that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. a²+b²=c²
- Intersecting lines
- 2 lines that have one common point
- Hypotenuse
- The side of a right triangle that is opposite the right angle. It is also the longest side.
- Similar polygons
- if the corresponding angles are congruent and the corresponding sides are proportional
- Median of a triangle
- Segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
- Congruent triangle
- when all pairs of corresponding angles are congruent and all pairs of sides are congruent
- square
- 2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles, 4 congruent sides, diagnals bisect angles, diagnals perpendicular, 4 right angles, diagnals congruent
- polygon
- a closed plane figure formed by two or more line segments
- vertex of a polygon
- on a polygon, the point where two sides intersect
- scalene triangle
- a triangle with no congurent sides
- Isosceles Triangle Theorem
- If two sides of a triangle are congruent the angle opposite them are congruent. Conversely, if 2 angles of a triangle are congruent then the sides opposite them must be congruent.
- corresponding angles
- A pair of angles which are on the same side of the transversal, one must be interior, one must be extirior, and they must be nonadjacent
- acute angle
- an angle that measures less than 90°
- SAS Congruence
- If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent
- Coordinates
- numbers that give an absolute location of a place
- Altitude of a triangle
- ⊥ segment from a vertex to a line containing the opposite side
- Perpendicular bisector
- A line that is perpendicular to a segment at its midpoint.
- line segment
- part of a line that extends from one endpoint to another
- AA similarity
- if two angles of a triangle are congruent to two angles of another triangle, the triangles are similar
- included angle
- an angle of a triangle that is formed by two sides of the triangle (where each of these sides is equal to a side in the other triangle).
- complementary angles
- two angles whose sums add to 90°
- circle
- the set of all points in a plane that are the same distance from a given point
- parallel
- lines in a plane that do not intersect
- use pythagorean theorem to classify triangles
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If c²=a²+b² then it is right. If c²>a²+b² then it is obtuse. If c²
- Transitive prop of parallel lines
- if 2 lines are ll to a third line then the are ll to each other
- Triangle inequality
- The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side.
- Parallelogram
- 2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles
- skew lines
- lines in a plane that are neither parallel nor intersecting
- Equiangular triangle
- A triangle with 3 congruent sides - also equilateral
- right triangle
- a triangle with one right angle made by the legs. The longest side which is opposite the right angle is the hypotenuse.
- regular polygon
- a polygon in which all sides are congruent and all angles are congruent
- SSS similarity
- if 3 sides of 1 triangle are in proportion to 3 sides of another triangle, the triangles are similar
- isosceles trapezoid
- one opposite side is parallel, one pair of opposite congruent angles, its base angles are congruent, its consecutive are supplementary, its diagonals are congruent, and it has exactly one line of symmetry
- SSS Triangle Congruence postulate
- If three sides of one triangle are congruent to three sides of a second triangle then the two triangles are congruent
- plane
- a perfectly flat surface that extends infinitely in all directions
- plane
- A flat surface that extends without end in all directions - determined by 3 points
- concave polygon
- at least one diagonal contains a point outside the polygon
- rectangle
- 2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles, 4 right angles, diagnals congruent
- vertical angles
- opposite angles formed by two intersecting lines
- Line intersection Postulate
- 2 lines intersect in exactly one point
- acute triangle
- a triangle with all acute angles
- Perimeters of similar polygons
- If 2 polygons are similar, then the ratio of the perimeters is equal to the ratio of their corresponding sides.
- trapezoid
- Quadrilateral with exactly one pair of parallel sides.
- Consecutive angles
- of a polygon are 2 sides that have a common endpoint
- angle
- a figure formed by two rays with a common endpoint, can be named by the vertex ∠A or by 3 point with the vertex in the middle ∠ABC
- rhombus
- 2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles, 4 congruent sides, diagnals bisect angles, diagnals perpendicular
- Parallel lines
- Coplanar lines that will never intersect - they are the same distance apart
- isosceles triangle
- a triangle with two congruent sides called legs, the non-congruent side is the base
- coplanar
- Figures that lie in the same plane.
- Angle Addition postulate
- if point B lies in the interior of angle AOC, then the m of angle AOB + the m of angle BOC = m of angle AOC
- SAS SImilarity
- if one angle of a triangle is congruent to an angle of another triangle, and the sides of each triangle adjacent to that angle are in proportion, the triangles are similar