Geometry Theorems and Definitions Flashcards

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Questions and Answers

What are definitions?

Definitions

What are complementary angles?

Two angles whose measures equal 90 degrees

What are supplementary angles?

Two angles whose measures equal 180 degrees

What is a theorem?

A statement that can be proven Signup and view all the answers

What are vertical angles?

Four angles formed by intersecting lines and facing in four different directions Signup and view all the answers

What is a transversal?

A line that intersects two lines in the same plane at different points Signup and view all the answers

What are corresponding angles?

Pairs of angles formed by two lines and a transversal that make an F pattern Signup and view all the answers

What are same-sided interior angles?

Pairs of angles formed by two lines and a transversal that make a C pattern Signup and view all the answers

What are alternate interior angles?

Pairs of angles formed by two lines and a transversal that make a Z pattern Signup and view all the answers

What are congruent angles?

Angles that are equal in measure Signup and view all the answers

What are similar triangles?

Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion Signup and view all the answers

What is an angle bisector?

A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure Signup and view all the answers

What is a segment bisector?

A ray, line or segment that divides a segment into two parts of equal measure Signup and view all the answers

What are the legs of an isosceles triangle?

The sides of equal measure in an isosceles triangle Signup and view all the answers

What is the base of an isosceles triangle?

The third side of an isosceles triangle Signup and view all the answers

What does equiangular mean?

Having angles that are all equal in measure Signup and view all the answers

What is a perpendicular bisector?

A line that bisects a segment and is perpendicular to it Signup and view all the answers

What is an altitude?

A segment from a vertex of a triangle perpendicular to the line containing the opposite side Signup and view all the answers

What is the geometric mean?

The value of x in the proportion a/x = x/b where a, b, and x are positive numbers Signup and view all the answers

What is sine (sin)?

For an acute angle of a right triangle, the ratio of the side opposite the angle to the measure of the hypotenuse Signup and view all the answers

What is cosine (cos)?

For an acute angle of a right triangle, the ratio of the side adjacent to the angle to the measure of the hypotenuse Signup and view all the answers

What is tangent (tan)?

For an acute angle of a right triangle, the ratio of the side opposite the angle to the measure of the side adjacent Signup and view all the answers

What are algebra postulates?

Algebra postulates Signup and view all the answers

What is the addition property of equality?

If the same number is added to equal numbers, then the sums are equal Signup and view all the answers

What is the subtraction property of equality?

If the same number is subtracted from equal numbers, then the differences are equal Signup and view all the answers

What is the multiplication property of equality?

If the same number is multiplied from equal numbers, then the products are equal Signup and view all the answers

What is the division property of equality?

If the same number is divided from equal numbers, then the quotients are equal Signup and view all the answers

What is the reflexive property of equality?

A number is equal to itself Signup and view all the answers

What is the symmetric property of equality?

If a = b, then b = a Signup and view all the answers

What is the substitution property of equality?

If values are equal, then one value may be substituted for the other Signup and view all the answers

What is the transitive property of equality?

If a = b and b = c, then a = c Signup and view all the answers

What is the distributive property of equality?

a(b + c) = ab + ac Signup and view all the answers

What are congruence postulates?

Congruence postulates Signup and view all the answers

What is the reflexive property of congruence?

a ≅ a Signup and view all the answers

What is the symmetric property of congruence?

If a ≅ b, then b ≅ a Signup and view all the answers

What is the transitive property of congruence?

If a ≅ b and b ≅ c, then a ≅ c Signup and view all the answers

What are angle postulates and theorems?

Angle postulates and theorems Signup and view all the answers

What is the angle addition postulate?

For any angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts Signup and view all the answers

What is the linear pair theorem?

If two angles form a linear pair, then they are supplementary Signup and view all the answers

Study Notes

Definitions and Key Concepts

Definitions provide the foundational terminology used in geometry studies.
Complementary angles are two angles that together measure 90 degrees.
Supplementary angles are two angles that together measure 180 degrees.
Theorem refers to a statement that can be logically proven.

Types of Angles

Vertical angles are formed by intersecting lines, creating four angles facing different directions.
A transversal is a line that intersects two other lines in the same plane at distinct points.
Corresponding angles are pairs formed by a transversal intersecting two lines, creating an F pattern.
Same-sided interior angles are formed by a transversal and two lines, creating a C pattern.
Alternate interior angles are another pair formed by a transversal and two lines, creating a Z pattern.

Triangle Properties and Definitions

Congruent angles refer to triangles with equal corresponding parts (sides and angles).
Similar triangles have corresponding angles that are equal and sides that are proportional.
An angle bisector divides an angle into two equal parts, originating from the angle's vertex.
A segment bisector divides a line segment into two equal parts.

Isosceles Triangle

Legs of an isosceles triangle are the two sides that are of equal length.
The base of an isosceles triangle is the third side, differing in length from the legs.

Angle Relationships

Equiangular means having all angles equal in measure.
A perpendicular bisector not only bisects a segment but is also perpendicular to it.
An altitude in a triangle extends from a vertex to the line containing the opposite side, forming a right angle.

Geometric Means and Trigonometric Functions

The geometric mean x satisfies the equation a/x = x/b for positive numbers a, b, and x.
Sine (sin) for an acute angle is the ratio of the opposite side to the hypotenuse.
Cosine (cos) for an acute angle is the ratio of the adjacent side to the hypotenuse.
Tangent (tan) for an acute angle is the ratio of the opposite side to the adjacent side.

Algebra Postulates

Algebra postulates serve as foundational rules in algebra.
The addition property states that adding the same number to equal quantities results in equal sums.
The subtraction property maintains that subtracting the same number from equal quantities results in equal differences.
The multiplication property indicates that multiplying equal quantities by the same number results in equal products.
The division property indicates that dividing equal quantities by the same number results in equal quotients.
Reflexive property states that any number is equal to itself.
Symmetric property indicates if a=b, then b=a.
Substitution property allows for one equivalent value to replace another in equations.
Transitive property holds that if a=b and b=c, then a=c.
Distributive property illustrates that a(b+c) equals ab + ac.

Congruence Properties

Congruence postulates define the criteria under which geometric figures are congruent.
The reflexive property of congruence states any figure is congruent to itself.
The symmetric property of congruence states if one figure is congruent to another, the reverse is also true.
Transitive property of congruence holds that if one figure is congruent to a second, and the second to a third, then the first is also congruent to the third.

Angle Theorems

Angle postulates and theorems include essential rules pertaining to angles.
The Angle Addition Postulate states that the measure of an angle equals the sum of its non-overlapping parts.
The Linear Pair Theorem states that if two angles form a linear pair, then they are supplementary.

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Description

Test your understanding of key geometry concepts with these flashcards. This quiz includes definitions of complementary angles, supplementary angles, vertical angles, and essential theorems. Perfect for students looking to reinforce their geometric knowledge.