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An angle whose measure is less than 90°

Acute Angle. An angle whose measure is less than 90°. Adjacent Angles. Two angles with a common vertex and a common side. Alternate Exterior Angles. 2 and 8 1 and 7.

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An angle whose measure is less than 90°

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  1. Acute Angle An angle whose measure is less than 90°

  2. Adjacent Angles Two angles with a common vertex and a common side.

  3. Alternate Exterior Angles 2 and 8 1 and 7 Two non-adjacent angles that lie on the opposite sides of a transversal outside two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

  4. Alternate Interior Angles 3 and 6 4 and 5 Two non-adjacent angles that lie on the opposite sides of a transversal between two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

  5. Angle X 3 V Z Formed by 2 rays (sides) with the same endpoint (vertex).

  6. Angle Addition Postulate If T is in the interior of ∠QRS, then m∠QRT+ m∠TRS= m∠QRS.

  7. Angle Bisector B A D C A ray that divides an angle into two congruent angles.

  8. Auxiliary Line A line (or ray or segment) added to a diagram to help in a proof or in determining the solution to a problem. DE is an auxiliary line.

  9. Biconditional Two statements connected by the words “if and only if.”

  10. Collinear Points that are on the same line. B C D A E A, B, C, and D are collinear points. A, B, C, D, and E are non-collinear points.

  11. Complementary Two angles whose measures have a sum of 90.

  12. Compound Statement A statement formed when two or more simple statements are connected as either a conditional (if-then), a biconditional (if and only if), a conjunction (and), or a disjunction (or).

  13. Conclusion The “then” statement in an if-then statement.

  14. Conditional Statement A statement that tells if one thing happens another will follow. Example: “If a polygon has three sides then it is a triangle.”

  15. Congruent Exactly equal in size and shape. Congruent segments have the same length. Congruent angles have the same measure.

  16. Congruent Angles Angles that have the same measure. X W

  17. Congruent Segments J K L M Segments that have the same length.

  18. Conjecture An educated guess, opinion, hypothesis.

  19. Conjunction Two statements joined by the word and, represented by the symbol ^.

  20. Contrapositive A version of a conditional statement formed by interchanging and negating both the hypothesis and conclusion of the statement.

  21. Converse A version of a conditional statement formed by interchanging the hypothesis and conclusion of the statement.

  22. Coplanar Lines Lines that are in the same plane.

  23. Coplanar Points Points that are in the same plane. F A C A, B, C, D, and E are coplanar points. A, B, C, D, E, and F are non-coplanar points. D B E

  24. Corresponding Angles 1 and 5 2 and 4 3 and 8 4 and 7 Two non-adjacent angles that lie on the same side of a transversal, in “corresponding” positions with respect to the two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

  25. Counterexample An example that shows that a conjecture is not always true.

  26. Deductive Reasoning The use of facts, definitions, rules and/or properties to prove that a conjecture is true.

  27. Disjunction The symbol v represents a disjunction, you read it as “or.”

  28. Distance Formula The distance between can be found using the formula

  29. Endpoint A point at one end of a segment or the starting point of a ray.

  30. Hypothesis The “if” clause in an if-then statement.

  31. Inductive Reasoning The process of observing data, recognizing patterns, and making a generalization.

  32. Inverse A version of a conditional statement formed by negating both the hypothesis and conclusion of the statement.

  33. Line A set of points that extends in 2 directions without end. m A B Line m or line AB or AB

  34. Line Segment Part of a line consisting of two endpoints and all points between them. N M Segment MN or Segment NM or MN or NM

  35. Linear Pair A pair of adjacent angles whose noncommon side are opposite rays.

  36. Logically Equivalent When two statements have the same exact truth values.

  37. Midpoint A B C A point that divides a segment into two congruent segments.

  38. Midpoint Formula The midpoint of a segement with endpoints can be found using the formula

  39. Negation of p The symbol ~p is the negation of p and can be read as “not p.”

  40. Obtuse Angle An angle whose measure is greater than 90° but less than 180°.

  41. Opposite Rays F H D Two collinear rays with the same endpoint. They always form a line. HF and HD are opposite rays.

  42. Parallel Lines a c Coplanar lines that do not intersect. a//c

  43. Parallel Planes W M Planes that do not intersect.

  44. Perpendicular Lines A C B 2 lines intersect to form right angles.

  45. Perpendicular Planes B D Planes intersect to form right angles.

  46. Plane A flat surface that extends in all directions without end. It has no thickness. W A B C Plane W or Plane ABC

  47. Point A location in space •A

  48. Postulate A statement that is accepted without proof.

  49. Proof An argument that transforms a conjecture to a theorem through the application of logical reasoning or deductive reasoning.

  50. Pythagorean Theorem For sides a, b, and c in a right triangle, a2 + b2 = c2.

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