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?
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What are vertical angles?
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What is a transversal?
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What are corresponding angles?
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What are same-sided interior angles?
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What are alternate interior angles?
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What are congruent angles?
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What are similar triangles?
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What is an angle bisector?
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What is a segment bisector?
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What are the legs of an isosceles triangle?
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What is the base of an isosceles triangle?
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What does equiangular mean?
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What is a perpendicular bisector?
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What is an altitude?
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What is the geometric mean?
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What is sine (sin)?
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What is cosine (cos)?
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What is tangent (tan)?
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What are algebra postulates?
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What is the addition property of equality?
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What is the subtraction property of equality?
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What is the multiplication property of equality?
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What is the division property of equality?
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What is the reflexive property of equality?
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What is the symmetric property of equality?
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What is the substitution property of equality?
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What is the transitive property of equality?
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What is the distributive property of equality?
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What are congruence postulates?
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What is the reflexive property of congruence?
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What is the symmetric property of congruence?
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What is the transitive property of congruence?
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What are angle postulates and theorems?
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What is the angle addition postulate?
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What is the linear pair theorem?
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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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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.