Burdge Geometry Final

space

The three-dimensional extension in which all objects exist and events occur.

collinear points

Points that lie on the same straight line.

coplanar points

Points that lie on the same plane.

intersection

The point or set of points where two or more geometric figures meet.

segment

A part of a line consisting of two endpoints and all points between them.

ray

A part of a line that starts at an endpoint and extends infinitely in one direction.

opposite ray

Two rays that share the same endpoint but extend in opposite directions.

postulate

statement accepted as fact without proof

midpoint of a segment

The point that divides a segment into two congruent segments.

bisector of a segment

A line, ray, or segment that divides the segment into two equal parts.

congruent

Figures or segments that have the same size and shape.

angle

A figure formed by two rays with a common endpoint.

sides of an angle

The two rays that form an angle.

vertex of an angle

The common endpoint of the two rays that form an angle.

acute angle

An angle that measures less than 90 degrees.

obtuse angle

An angle that measures more than 90 degrees but less than 180 degrees.

right angle

An angle that measures exactly 90 degrees.

congruent angles

Angles that have the same measure.

adjacent angles

Angles that share a common side and a common vertex.

bisector of an angle

A ray that divides an angle into two equal angles.

complementary angles

Two angles whose measures add up to 90 degrees.

supplementary angles

Two angles whose measures add up to 180 degrees.

vertical angles

Angles that are opposite each other when two lines intersect.

perpendicular lines

Lines that intersect to form right angles.

parallel lines

Lines in a plane that never intersect and are always the same distance apart.

skew lines

Lines that do not intersect and are not parallel.

parallel planes

Planes that do not intersect.

transversal

A line that intersects two or more lines at different points.

alternate interior angles

Angles that lie on opposite sides of the transversal and inside the two lines.

same-side interior angles

Angles that lie on the same side of the transversal and inside the two lines.

corresponding angles

Angles that are in the same position on two different lines in relation to a transversal.

triangle

A polygon with three sides and three angles.

vertex of a triangle

A corner point where two sides of a triangle meet.

sides of a triangle

The three line segments that form the triangle.

scalene triangle

A triangle with all sides of different lengths.

isosceles triangle

A triangle with at least two sides of equal length.

equilateral triangle

A triangle with all three sides of equal length.

acute triangle

A triangle with all angles measuring less than 90 degrees.

obtuse triangle

A triangle with one angle measuring more than 90 degrees.

right triangle

A triangle with one angle measuring exactly 90 degrees.

equiangular triangle

A triangle with all angles equal.

auxiliary line

A line added to a diagram to help in proof or explanation.

exterior angles of a triangle

Angles formed outside a triangle when one side is extended.

remote interior angles

The two interior angles of a triangle that are not adjacent to a given exterior angle.

polygon

A closed figure with three or more sides.

convex polygon

A polygon where all interior angles are less than 180 degrees.

diagonal

A segment that connects two non-adjacent vertices of a polygon.

regular polygon

A polygon with all sides and angles equal.

inductive reasoning

A type of reasoning that involves drawing general conclusions from specific examples. I don’t think you have to know this but it was on the vocab sheet.

congruent triangles

Triangles that have the same size and shape.

line perpendicular to a plane

A line that intersects a plane at a right angle.

legs of an isosceles triangle

The two equal sides of an isosceles triangle.

base of an isosceles triangle

The side of an isosceles triangle that is not equal to the other two sides.

hypotenuse

The longest side of a right triangle, opposite the right angle.

legs of a right triangle

The two sides of a right triangle that form the right angle.

median of a triangle

A line segment from a vertex to the midpoint of the opposite side.

altitude of a triangle

The perpendicular segment from a vertex to the line containing the opposite side.

perpendicular bisector of a segment

A line that is perpendicular to a segment at its midpoint.

the distance from a point to a line

The length of the perpendicular segment from the point to the line.

parallelogram

A four-sided figure with opposite sides parallel and equal.

rectangle

A parallelogram with four right angles.

rhombus

A parallelogram with all sides equal.

square

A rectangle with all sides equal.

trapezoid

A four-sided figure with one pair of parallel sides.

bases of a trapezoid

The two parallel sides of a trapezoid.

legs of a trapezoid

The non-parallel sides of a trapezoid.

isosceles trapezoid

A trapezoid with non-parallel sides that are equal in length.

median of a trapezoid

A line segment that connects the midpoints of the legs of a trapezoid.

midsegment of a triangle

a line that connects the midpoints of two sides in a triangle

ratio

A comparison of two quantities by division.

proportion

An equation that states that two ratios are equal.

means

The middle terms of a proportion.

extremes

The outer terms of a proportion.

similar polygons

Polygons that have the same shape (and congruent angles) but may have different sizes.

scale factor

The ratio of the lengths of corresponding sides of similar figures.

line

Through any two points, there is exactly one ___.

plane

There is at least one ___ through any three points, and there is exactly one ___ through any three noncollinear points (both blanks are the same so just write it once).

point

If two lines intersect, then they intersect at exactly one ___.

transversal, congruent

If two lines are cut by a ___ and the corresponding angles are ___, the lines are parallel.

parallel

If two ___ lines are cut by a transversal, then the corresponding angles are congruent.

transversal, angles

If two parallel lines are cut by a ____, then the alternate interior ____ are congruent.

supplementary

If two parallel lines are cut by a transversal, then the same-side interior angles are ___.

supplementary, parallel

If two lines are cut by a transversal and the same-side interior angles are ___, then the lines are ___.

perpendicular

In a plane, two lines ___ (it’s not parallel, although that is correct) to the same line are parallel.

parallel

If two parallel planes are cut by a third plane, then the lines of intersection are ___.

equidistant

If two lines are parallel, all points on one line are ___ from the other line.

congruent

If three parallel lines cut off congruent segments on one transversal, then they cut off ___ segments on every transversal.

three, congruent

If ___ (write out the number in letters) sides of one triangle are congruent to three sides of another triangle, then the triangles are ___.

two, angle, congruent

If ___ (write out the number in letters) sides and the included ___ of one triangle are congruent to ___ sides and the included ___ of another triangle, then the triangles are ___ (for the repeating terms, just write them once—in order though).

two, side, congruent

If ___ (write out the number in letters) angles and the included ___ of one triangle are congruent to ___ angles and the included ___ of another triangle, then the triangles are ___ (for the repeating terms, just write them once—in order though).

angles, side, congruent

If two ___ and a non-included ___ of one triangle are congruent to the corresponding parts of another triangle, then the triangles are ___.

hypotenuse, congruent

If the ___ and a leg of one triangle are congruent to the corresponding parts of another right triangle, then the triangles are ___.

similar

If two angles of one triangle are congruent to two angles of another triangle, the triangles are ___.

proportion, similar

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in ___, then the triangles are ___.

proportion, similar

If the sides of two triangles are in ___, then the triangles are ___.

180

The sum of the measures of the angles in a triangle is ___°.

exterior, remote

The measure of an ___ angle of a triangle equals the sum of the measures of the two ___ interior angles.

parallel, half

The segment that joins the midpoints of two sides of a triangle is ___ to the third side and ___ as long as the third side.

proportional

If a ray bisects an angle of a triangle, then it divides the opposite side into segments ___ to the other two sides.

larger

If one side of a triangle is longer than another, the angle opposite the longer side is ___ (smaller/larger).