Geometry Basics Chapter 1-2 Flashcards
Altitude to a side of a triangle
A segment from a vertex perpendicular to the opposite side
How many lines can be drawn through any two points?
One and only one
AB is the only line that can be drawn between A and B
Right Angle
An angle that measures 90 degrees
Right Triangle
A triangle having a right angle
Postulate 9: Powers Postulate
Like powers of equals are equal.
If a=b then a squared=b squared
Principle of Pairs of Angles: If angle of c degree is cut into two adjacent angles of a degree and b degree…
then a degree+b degree=c degree
Principle of Pairs of Angles
Hypotenuse
The longest side of a triangle
How many bisectors are in an angle?
One and only one
Only AD is the bisector of angle A
True/False: A geometric figure can be moved without change in size or shape?
True
If a Line Segment is divided into two equal parts
The point of division is the midpoint of the line segment
The line that crosses at the midpoint is said to bisect the segment
Complementary Angles
Complementary Angles are two angles whose measure total 90 degrees
If a line segment is divided into parts
The length of the whole line segment equals the sum of the length of its parts.
The length of the whole line segment is greater than the length of any part
Perpendicular
Lines, rays, or segments that meet at right angles.
Isosceles Triangle
A triangle having at least two congruent sides
The equal sides are called the legs
The remaining side is called the base
Angles on either side of the base are base angles
Angle opposite the base is the vertex angle
Postulate 4: Reflexive Postulate or Identity Postulate
Any quantity equals itself
X=X, AB=AB, angle A=angle A
Angle
An angle is the figure formed by two rays with a common end point. The rays are the sides of the angle, while the end point is its vertex.
Postulate 2: Substitution Postulate
A quantity may be substituted for its equal in any expression or equation.
If x=5 and y=x+3, we may substitute 5 for x and find y=5+3=8
Scalene Triangle
A triangle having no congruent sides
Central Angle
An angle formed by two radii
All Vertical angles
Are Congruent
Chord
A segment joining any two points on a circle
Point
Point has position only. It has no length, width, or thickness. A point is represented by a dot. A point is designated by a capital letter next to the dot.
Postulate 13: The length of a segment is the…
Shortest distance between two points
AB is shorter than the curved or broken line segment between A and B
Theorem
A statement, which when proved, can be used to prove other statements or derive other results. Each basic theorems requires the use of definitions and postulates for its proof.
Radius
A segment joining the center of a circle to a point on the circle.
The def of a circle, it follows that the radii of a circle are congruent.
Postulate 16: How many midpoints are on a given segment?
One and only one
Quadrilateral
A polygon having four sides
Postulate 14: How many circles can be drawn with any given point as center and a given line segment as a radius?
one and only one circle
only circle A can be drawn with A as center and AB as a radius
Adjacent Angles
Two angles that share the same vertex and have a common side between them.
Altitudes of obtuse triangle
Altitude drawn to either side of the obtuse angle fall outside the triangle
Thus in obtuse triangle ABC (shaded), altitudes BD and CE fall outside the triangle. In each case, a side of the obtuse angle must be extended
Plane Surface
A plane surface is a surface such that a straight line connecting any two of its points lies entirely in it. A plane is a flat surface.
Angle Bisector of a triangle
A segment or ray that bisects an angle and extends to the opposite side
BD the angle bisector of angle B, Bisects angle B making angles 1 and 2 congruent.
Median of a Triangle
A segment from a vertex to the midpoint of the opposite side
BM, the median to AC, bisects AC, making AM=MC
What does it mean to have supplementary angles that are congruent?
Each of the angles is a right angle
Diameter
A diameter is a chord through the center of the circle
The longest chord
Twice the length of the radius
Obtuse Angle
An angle whose measure is more than 90 degrees and less than 180 degrees.
Straight Line
are unlimited in extent and may extend in either direction infinetly.
Surface
A surface has length and width but no thickness.
Congruent Angles
Angles that have the same number of degrees
When are adjacent angles supplementary?
If their exterior sides lie in the same straight line
What is the distance around the circle?
The Circumference (360 degrees)
Pentagon
A polygon of five sides
Obtuse triangle
A triangle having an obtuse angle
Perpendicular bisector of a side
A line that bisects and is perpendicular to a side
PQ, the perpendicular bisector of AC, bisects AC and is perpendicular to it
Particular Statement
Statement about one or some of the members of the set or class referred to in the general statement: All greyhounds are dogs.
If two supplementary angles contain a degree and b degree…
Then a degree + b degree = 180 degree
Postulate 10: Roots Postulate
Like roots of equals are equal
Straight Angle
An angle that measures 180 degrees
Postulate 5: Addition Postulate
If equals are added to equals, the sums are equal
if a=b and c=d then a+c=b+d
Postulate 6: Subtraction Postulate
If equals are subtracted from equals, the differences are equal
if a=b and c=d, then a-c=b-d
Supplementary Angles
Supplementary Angles are two angles whose measures total 180 degrees
Postulate 18: Through any point on a line, how many perpendiculars can be drawn to the line?
One and only one
Only PC is perpendicular to AB at point P on AB
Postulate 1: Transistive Postulate
Things equal to the same or equal things are equal to each other
If a=b and c=b, then a=c
If two complementary angles contain a degree and b degree
then a degree + b degree = 90 degrees
Principles of Pairs of Angles
Supplements of the same angle are…
Congruent
angle a is congruent to angle b and each is the supplement of angle x
Postulate 3: Partition Postulate
The whole equals the sum of its parts
the total value of a dime, a nickel, and a penny is 16 cents
Equilateral Triangle
A triangle having three congruent sides
AKA an isoceles triangle
Arc
An arc is a continuous part of a circle.
Deduction
Follows logically when the general statement is applied to the particular statement: All greyhounds are quadrupeds
All straight angles are…
Congruent
Vertical Angles
Vertical angles are two non adjacent angles formed by two intersecting lines
Complements of congruent angles are….
Congruent
angle c is congruent to angle d and their complements are the congruent angles x and y
Acute Angle
An acute angle is an angle whose measure is less than 90 degrees.
Acute Triangle
A triangle having three acute angles
General Statement
referring to a whole set or class of things, such as the class of dogs: All dogs are quadrupeds
Ray
Ray is the part of a straight line beginning at a given point and extending limitlessly in one direction.
A line that bisects an angle
Divides it into two congruent parts
Postulate 8: Division Postulate
If Equals are divided by equals, the quotients are equal
if a=b and c=d, then a/c=b/d
True or False: Vertical angles are not congruent
False
angle a= angle b; this follows principle 4 (supplements of the same angle are congruent), since angle a and angle b are supplements of the same angle, angle c
How many points can two lines intersect?
One and only one point
Only P is the point of intersection of AB and CD
Polygon
A closed plane figure bounded by straight line segments as sides
Semicircle
An arc measuring one-half of the circumference of a circle and thus contains 180 degrees.
(a diameter divides a circle into two semicircles)
Line
A line has length but has no width or thickness.
A line may be straight, curved, or a combination of these.
Circle
A circle is the set of all points in a plane that are the same distance from the center.
Supplements of congruent angles are…
Congruent
angle c is congruent to angle d and their supplements are the congruent angles x and y.
Triangle
A polygon having three sides whose degrees allways measure 180.
When are Adjacent angles complementary ?
If their exterior sides are perpendicular
Vertex of a triangle
A point at which two of the sides of the triangle meet
Compliments of the same angle are….
Congruent
angle a is congruent to angle b and each is the compliment of angle x
Through any point outside a line, how many perpendiculars can be drawn to a given line?
One and only one
All right angles are….
Congruent
Postulate 7: Multiplication Postulate
If equals are multiplied by equals, the products are equal;
if a=b and c=d, then ac=bd
Perpendicular Bisector
A perpendicular bisector of a given segment is perpendicular to the segment and bisects it.
What does it mean to have two line segments having the same length?
Congruent
