Questions and Answers
What does the Angle Addition Postulate state?
The measure of the larger angle is the sum of the measures of the two smaller angles.
What does the Linear Angle Theorem state?
If two angles form a linear pair, then they are supplementary.
What is the Transitive Property of Equality?
If a = b and b = c, then a = c.
What is the Definition of a Segment Bisector?
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What does the Property of Substitution state?
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Match the following properties of equality with their examples:
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What does the Vertical Angle Theorem state?
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What is the Definition of Supplementary Angles?
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What is the Definition of an Angle Bisector?
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What does the Definition of Congruency state?
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What does the Corresponding Angle Postulate state?
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What does the Alternate Interior Angle Conjecture state?
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What does the Alternate Exterior Angle Theorem state?
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What is the Same Side Interior Angle Theorem?
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What does the Converse of the Corresponding Angle Postulate state?
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What does the Converse of the Alternate Interior Angle Postulate state?
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What does the Converse of the Alternate Exterior Angle Postulate state?
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What does the Triangle Sum Theorem state?
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What is the Definition of Perpendicular Lines?
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What does the 2 Lines Perpendicular Theorem state?
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What does the All Right Angles are Congruent state?
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What does the 2 Lines Parallel Theorem state?
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What does the SSS Postulate state?
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What does the SAS Postulate state?
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What does the Angle Side Angle Postulate (ASA) state?
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What does the Angle Side Side Postulate (ASS) OR Side Side Angle Postulate (SSA) state?
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What does the Angle Angle Side Postulate (AAS) state?
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What is the Reflexive Property?
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What does the Overlapping Line Segment Theorem state?
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What does the Hypotenuse Leg theorem state?
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What is the Definition of a Right Triangle?
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What does the Definition of a Midpoint state?
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What does the Congruent Parts Congruent Triangles Congruent (CPCTC) state?
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What does the Isosceles Triangle Theorem (ITT) state?
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What does the Converse of ITT state?
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Study Notes
Angle Addition Postulate
- States that if point B is in the interior of angle AOC, then the measure of angle AOC equals the sum of the measures of angles AOB and BOC.
Linear Angle Theorem
- Asserts that when two angles form a linear pair, they are supplementary, meaning their measures add up to 180 degrees.
Transitive Property of Equality
- If two values are equal to a third value, then they are equal to each other (if a = b and b = c, then a = c).
Definition of Segment Bisector
- Defined as a point, segment, line, or plane that divides a line segment into two equal halves, always including the midpoint.
Property of Substitution
- If one variable is equal to another, it can be replaced in any equation, allowing interchangeable use of these variables.
Properties of Equality
- Includes rules for effective algebra manipulation:
- Addition: x - 5 = 10 leads to x = 15.
- Subtraction: x + 5 = 10 results in x = 5.
- Multiplication: r/3 = 4 implies r = 12.
- Division: 2x = 16 gives x = 8.
Vertical Angle Theorem
- States that if angle A and angle B are vertical angles, then angle A is congruent to angle B.
Definition of Supplementary Angles
- Two angles are supplementary if their measures sum to 180 degrees.
Definition of an Angle Bisector
- A ray, line, or segment that divides an angle into two equal parts, ensuring the two resulting angles are congruent.
Definition of Congruency
- States that if segment AB is congruent to segment BC, then their lengths are equal (AB = BC).
Definition of Congruence
- Similar to congruency, reinforces that if two segments are congruent, they are equal in length.
Corresponding Angle Postulate
- When two parallel lines are crossed by a transversal, the corresponding angles are congruent.
Alternate Interior Angle Conjecture
- Asserts that alternate interior angles are congruent when two parallel lines are intersected by a transversal.
Alternate Exterior Angle Theorem
- States that alternate exterior angles are congruent when two parallel lines are cut by a transversal.
Same Side Interior Angle Theorem
- States that if two parallel lines are intersected by a transversal, then the same side interior angles are supplementary.
Converse of the Corresponding Angle Postulate
- States that if corresponding angles are congruent, then the two lines are parallel.
Converse of the Alternate Interior Angle Postulate
- States that if a transversal creates congruent alternate interior angles, then the two lines must be parallel.
Converse of the Alternate Exterior Angle Postulate
- If alternate exterior angles are congruent, then the two lines cut by the transversal are parallel.
Triangle Sum Theorem
- States that the sum of the interior angles of a triangle is always 180 degrees.
Definition of Perpendicular Lines
- When two lines intersect to form right angles, they are considered perpendicular. If one angle is right, the lines are perpendicular.
2 Lines Perpendicular Theorem
- If two lines are both perpendicular to the same line, then they are parallel to each other.
All Right Angles are Congruent
- All right angles (90 degrees) measure the same and are therefore congruent.
2 Lines Parallel Theorem
- If two lines are parallel to a third line, they are parallel to each other.
SSS Postulate (Side Side Side)
- If all three sides of two triangles are congruent, then the triangles themselves are congruent.
SAS Postulate (Side Angle Side)
- If two sides and the included angle of one triangle are congruent to those of another triangle, then the triangles are congruent.
Angle Side Angle Postulate (ASA)
- If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Angle Side Side Postulate (ASS) or Side Side Angle Postulate (SSA)
- States that if two angles and a non-included side of one triangle are congruent to those of another triangle, the triangles are congruent.
Angle Angle Side Postulate (AAS)
- If two angles and a corresponding non-inclusive side of one triangle are congruent to those of another triangle, then the triangles are congruent.
Reflexive Property
- A segment is congruent to itself (e.g., segment RN is congruent to segment RN).
Overlapping Line Segment Theorem
- If two overlapping segments share congruent non-overlapping parts, the entire segments are congruent.
Hypotenuse Leg
- If two right triangles have a congruent hypotenuse and one corresponding leg, then the triangles are congruent.
Definition of Right Triangle
- A triangle that contains a right angle (90 degrees).
Definition of a Midpoint
- The exact middle point of a line segment, splitting it into two equal parts.
Congruent Parts Congruent Triangles Congruent (CPCTC)
- If two triangles are congruent, then each corresponding part (angles and sides) is also congruent.
Isosceles Triangle Theorem (ITT)
- If two sides of a triangle are congruent, then the angles opposite those sides are also congruent.
Converse of ITT
- If two angles of a triangle are congruent, then the sides opposite those angles must also be congruent.
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Description
This quiz focuses on key concepts in algebraic and geometric proofs, including the Angle Addition Postulate, Linear Angle Theorem, and Transitive Property of Equality. Ideal for students looking to reinforce their understanding of foundational mathematical principles.