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Geometry Concepts #s 1-7.
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Terms in this set (92)
If you split a cone perpendicular to its base, what do you get?
A triangle.
If you split a cone parallel to its base, what do you get?
A circle.
What is a right triangle?
A triangle containing one 90 degree angle.
What does a cone on top of a sphere look like?
A hat on a person's head.
A line segment whose endpoints are on the edge of a circle is...
A chord.
A line segment that connects the centre of a circle to a point on the edge (half a diameter), is...
A radius.
The set of all points in a plane at a given distance (a radius) from a given point (centre) in the plane is...
A circle.
A chord that passes through the centre of a circle is...
A diameter.
Two or more circles with the same radius measure are...
Congruent Circles.
Concentric Circles are...
Two or more coplanar circles with the same centre.
An Arc of a Circle is...
Two points on a circle and all of the points between them along the circle.
A tangent is...
A line that intersects a circle exactly once.
A Semicircle is...
An arc with endpoints as the endpoint of the diameter.
An arc that is smaller than a semicircle is...
A minor arc.
An arc that is larger than a semicircle is...
A major arc.
A line that intersects a circle exactly twice is...
A secant.
An Inscribed Angle is...
An angle formed from two chords (or two secants) whose vertex is on the edge of the circle.
A Central Angle is...
An angle whose vertex is at the centre of a circle.
What are the three "undefined terms" of geometry?
Points, lines, and planes.
An angle is...
Two rays that share a common endpoint.
A straight arrangement of points; infinitely many points side by side; infinite length, but no thickness; extends forever is what?
A line.
A plane is...
A flat surface that extends forever; has length and width, but no thickness.
Basic unit of geometry - has no size, only location...
A point.
Two points and all the points in between them is...
A line segment.
Coplanar points are...
Points that lie on the same plane.
Collinear Points are...
Points that lie on the same line.
A ray is...
Part of a line; begins at one point and continues forever in one direction.
What is the midpoint formula?
(x1+x2/2, y1+y2/2)
What is the midpoint of a segment?
The midpoint of a segment is the point on the segment that is the same distance from one endpoint and another endpoint.
Two segments that have the same measure in length.
Congruent Segments.
What are Congruent Angles?
Two angles that have the same measurement.
The Angle Bisector is...
A ray that divides an angle into two congruent angles.
If two planes do not intersect then they are parallel. True or False?
True.
What is an Undecagon?
A polygon with 11 sides.
A closed shape with 3 or more straight line segments is...
A polygon.
All supplementary angles are linear pairs. True or False?
False.
All linear pairs are supplementary angles. True or False?
True.
Consider the line segment AT and point C. Must the following statement be true?
If CA = CT, then C is the midpoint of AT.
The statement doesn't have to be true because A, C, and T might not be collinear.
Two lines that are not parallel, are in different planes, and do not intersect are...
Skew Lines.
Are vertical angles consecutive angles?
No, because they are not next to each other.
What is a shape with 5 sides?
A pentagon.
If you cut a sphere parallel or perpendicular to the base, what 2-D shape do you get?
A circle.
If you cut a hemisphere perpendicular to the base, what 2-D shape do you get?
A parabolic shape. Nothing you really need to know.
If you cut a cylinder parallel to the base, what shape will you get?
A circle.
A net is...
A 2-dimensional pattern that you can cut and fold to form a 3-dimensional figure.
The 2-D shape you see when you "slice" a 3-D figure with a plane is...
A section.
Solid of Revolution is...
The 3-D solid/figure formed by spinning a 2-D figure on an imaginary axis.
If you do solid of revolution to a rectangle, what do you get?
A cylinder.
Isosceles Triangle is...
A triangle with two congruent sides.
A triangle with no congruent sides is...
A scalene triangle.
A triangle with 3 acute angles is...
An acute triangle.
An obtuse triangle is...
A triangle with exactly one obtuse angle.
What is a regular quadrilateral?
A square. (A parallelogram that is both equilateral and equiangular.)
A quadrilateral with exactly one pair of parallel sides is...
A trapezoid.
What is a rhombus?
A parallelogram that is equilateral.
What is the median of a triangle?
A line segment that connects the vertex to the midpoint of the opposite side.
What is the altitude of a triangle?
A line segment that connects the vertex to the opposite side and is perpendicular to it.
A quadrilateral with two distinct pairs of congruent sides.
A kite.
A rectangle is...
A parallelogram that is equiangular.
What is a parallelogram?
A quadrilateral with two pairs of parallel sides.
A polygon with six sides is...
A hexagon.
A heptagon is...
A 7 sided polygon.
A twelve sided polygon is called...
A dodecagon.
Only one line can be drawn through two different points. True or False?
True.
If two lines do not intersect, then they are parallel. True or False?
False. They can be skew lines.
If a line is perpendicular to two lines in a plane, but the line is not contained in the plane, then the line is perpendicular to the plane. True or False?
True.
Only one plane can pass through one line and a point that is not on the line. True or False?
True.
Adjacent angles are...
Two angles that have a common side and a common vertex and don't overlap. (There is no necessary relationship between adjacent angles.)
What is an obtuse angle?
An angle greater than 90˚ and less than 180˚.
What is an acute angle?
An angle with a degree measure below 90 degrees, but above 0 degrees.
A linear pair of angles is...
Two angles that share a vertex and a common side and their non-common sides form a line. (A linear pair of angles is supplementary.)
Vertical angles are...
Two angles formed by two intersecting lines and share a common vertex, but not a common side. (Pairs of vertical angles are equal in measure.)
Consecutive vertices are...
Two vertices of a polygon that are connected by a side.
Two angles of a polygon that share a common side are...
Consecutive Angles.
The diagonal of a polygon is...
A line segment connecting two non-consecutive vertices in the polygon.
What is a convex polygon?
A polygon with NO diagonals outside of the polygon.
What is a polygon with at least one diagonal outside the polygon?
Concave Polygon.
What is an equilateral polygon?
A polygon with sides that are all equal in measure.
What is an equiangular polygon?
A polygon with angles that are all equal in measure.
A polygon that is both equilateral AND equiangular is a...
Regular Polygon.
Anything polygon that is above a dodecagon is a...
n-gon.
A polygon with 10 sides is a...
Decagon.
What is a polygon with nine sides?
It is a Nonagon.
A polygon with 3 sides is a...
Triangle.
What is a polygon with 8 sides?
An Octagon.
A polygon with 4 sides is a...
Quadrilateral.
A line segment has an endpoint of (-4, 9) and (14, -3). What is the midpoint?
The midpoint is (5, 3).
A line segment has an endpoint of (-5, 16) and a midpoint of (8, -24). Find the other endpoint.
The endpoint is (21, -64).
Give the supplement to an angle of 67 degrees.
The supplement to the angle of 67 degrees is 113 degrees.
Give the compliment to an angle of 78 degrees.
The compliment to the angle of 78 degrees is 12 degrees.
What is space?
The set of all points in three dimensions. (The set of all points.)
What is Isometric Drawing?
A 2-D drawing of a 3-dimensional figure, showing 3 sides of an object in one view.
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