Geometry Proof Terms Flashcards
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Questions and Answers

What is the definition of Midpoint?

A point which divides a segment into 2 congruent segments.

What is the definition of Segment Bisector?

A line, segment, or plane that goes through the midpoint of a segment.

What is the definition of Angle Bisector?

A ray, a plane, a line, or a segment that divides an angle into 2 congruent angles.

What is the definition of Right Angle?

<p>90 degree angle.</p> Signup and view all the answers

What are Complementary Angles?

<p>2 angles that add up to 90 degrees.</p> Signup and view all the answers

What are Supplementary Angles?

<p>2 angles that add up to 180 degrees.</p> Signup and view all the answers

What does Congruence mean?

<p>An angle, shape, segment, or etc. that is the same size, shape, and measure. Expressed as ≅.</p> Signup and view all the answers

What are Perpendicular Lines?

<p>2 rays or lines that intersect to form right angles.</p> Signup and view all the answers

What is the Segment Addition Postulate?

<p>If B is between A and C, then AB + BC = AC.</p> Signup and view all the answers

What is the Angle Addition Postulate?

<p>If a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR = ∠PQR.</p> Signup and view all the answers

Any 2 points are located on the same line.

<p>True</p> Signup and view all the answers

What does the Midpoint Theorem state?

<p>If a point is the midpoint of a segment, the two segments that make up the segment are congruent to each other.</p> Signup and view all the answers

What does the Supplement Theorem state?

<p>If 2 angles form a linear pair then they are supplementary (180 degrees).</p> Signup and view all the answers

What does Congruent Supplement Theorem state?

<p>If the m∠1 + m∠2 = 180 and m∠2 + m∠3 = 180 then ∠1 ≊ ∠3.</p> Signup and view all the answers

What does the Perpendicular Line Form Right Angles Theorem state?

<p>If line AC ⊥ line DB, then ∠1, ∠2, ∠3, ∠4 are right angles.</p> Signup and view all the answers

What does the All Right Angles are Congruent Theorem state?

<p>If ∠1, ∠2, ∠3, ∠4 are all right angles, then ∠1 ≊ ∠2 ≊ ∠3 ≊ ∠4.</p> Signup and view all the answers

What does the 2 Angles that are Supplementary and Congruent then both are Right Angles Theorem state?

<p>If ∠5 ≊ ∠6 and ∠5 is supplementary, then each angle is a right angle.</p> Signup and view all the answers

What does the 2 Congruent Angles that form a Linear Pair are Right Angles Theorem state?

<p>If ∠7 and ∠8 form a linear pair, then ∠7 and ∠8 are right angles.</p> Signup and view all the answers

What is the Complement Theorem?

<p>If the non-common sides of 2 adjacent angles form a right angle, then the angles are complementary.</p> Signup and view all the answers

Vertical angles are congruent.

<p>True</p> Signup and view all the answers

What does the Perpendicular Lines form Congruent Adjacent Angles Theorem state?

<p>If two lines are perpendicular to one another then they form 2 congruent adjacent angles (90 degree angles).</p> Signup and view all the answers

What does the Common Segment Theorem state?

<p>If segment PR ≊ segment QS, then segment PQ ≊ segment RS.</p> Signup and view all the answers

What does the Common Angle Theorem state?

<p>If ∠PRT ≊ ∠SRQ then ∠PRS ≊ ∠TRQ.</p> Signup and view all the answers

What is the Addition Property?

<p>If a = b, then a + c = b + c.</p> Signup and view all the answers

What is the Subtraction Property?

<p>If a = b, then a - c = b - c.</p> Signup and view all the answers

What is the Symmetry Property?

<p>If a = b, then b = a.</p> Signup and view all the answers

What is the Distributive Property?

<p>a(b + c) = ab + ac.</p> Signup and view all the answers

What is the Reflexive Property?

<p>a = a.</p> Signup and view all the answers

What is the Transitive Property?

<p>If a = b and b = c then a = c.</p> Signup and view all the answers

What is the Multiplication Property?

<p>If a = b then a * c = b * c.</p> Signup and view all the answers

What is the Division Property?

<p>If a = b and c ≠ 0, then a/c = b/c.</p> Signup and view all the answers

What is the Substitution Property?

<p>If a = b then a may be replaced by b in any equation or expression.</p> Signup and view all the answers

Study Notes

Geometry Proof Terms

  • Midpoint: Point dividing a segment into two equal parts.
  • Segment Bisector: A line, segment, or plane passing through the midpoint, effectively bisecting the segment.
  • Angle Bisector: A ray, line, or segment that divides an angle into two equal angles.
  • Right Angle: An angle measuring 90 degrees.
  • Complementary Angles: Two angles whose measures add up to 90 degrees.
  • Supplementary Angles: Two angles whose measures sum to 180 degrees.
  • Congruence: Indicates that angles, shapes, or segments have the same size and measure, denoted by ≅.
  • Perpendicular Lines: Two lines or rays that intersect to form right angles.
  • Segment Addition Postulate: If point B lies between A and C, then ( AB + BC = AC ).
  • Angle Addition Postulate: If point S is in the interior of angle PQR, then ( \angle PQS + \angle SQR = \angle PQR ).
  • 2 Points are Always Collinear Postulate: Any two points are always on the same straight line.
  • Midpoint Theorem: A segment's midpoint creates two congruent segments.
  • Supplement Theorem: Two angles forming a linear pair are supplementary (sum to 180 degrees).
  • Congruent Supplement Theorem: If two angles both sum with another to 180 degrees, they are congruent.
  • Perpendicular Line Form Right Angles Theorem: Intersecting lines at right angles create four right angles.
  • All Right Angles are Congruent Theorem: All right angles are congruent to each other.
  • 2 Angles that are Supplementary and Congruent then both are Right Angles Theorem: Supplementary and equal angles are right angles.
  • 2 Congruent Angles that form a Linear Pair are Right Angles Theorem: Congruent angles forming a linear pair must be right angles.
  • Complement Theorem: If the non-common sides of two adjacent angles form a right angle, the angles are complementary.
  • Vertical Angles are Congruent Theorem: Vertical angles are congruent.
  • Perpendicular Lines form Congruent Adjacent Angles Theorem: Perpendicular lines create two congruent adjacent right angles.
  • Common Segment Theorem: If two segments are congruent, the segments connecting their endpoints will also be congruent.
  • Common Angle Theorem: If two angles share a common angle and are congruent, their measures are also equal.
  • Addition Property: If two quantities are equal, adding the same quantity to both maintains equality.
  • Subtraction Property: Subtracting the same quantity from two equal quantities sustains equality.
  • Symmetry Property: If one quantity equals another, the reverse is also true.
  • Distributive Property: The product of a number with a sum equals the sum of the products.
  • Reflexive Property: Any quantity equals itself.
  • Transitive Property: If one quantity equals a second, which also equals a third, the first equals the third.
  • Multiplication Property: If two quantities are equal, multiplying both by the same number remains equal.
  • Division Property: If two quantities are equal and the divisor is not zero, dividing both maintains equality.
  • Substitution Property: A quantity equal to another can be substituted into any expression or equation.

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Test your knowledge of key geometry proof terms with these flashcards! Learn definitions for concepts such as midpoint, segment bisector, and angle bisector. Perfect for students looking to strengthen their understanding of geometry.

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