1st Semester Key Definitions, Properties, and Theorems

  1. Definition of Congruent- If measures are equal, two angles are congruent or if lengths are equal, segments are congruent.
  2. Definition of Bisect: Bisect means to cut something into two congruent parts.
  3. Angle Bistector- a segment, line, or ray that splits an angle into two congruent angles.
  4. Segment Bisector- a segment, line, or ray that splits a segment into two congruent parts.
  5. Definition of Midpoint- A midpoint splits a line segment into two congruent segments.
  6. Definition of Supplementary- Two or more angles whose sum is 180 degrees.
  7. Reflexive property- a line segment or angle is congruent to itself.  Any value is equal to itself.
  8. Transitive property- If A=B and B=C, then A=C (also works for congruence).
  9. Substitution property of equality- If a=b, you can substitute a for b or b for a in any equation.
  10. Angle Addition Postulate- If an angle is split into parts, the sum of the measures of the parts equal the measure of the original angle
  11. Linear Pair Theorem- If two angles form a linear pair, then they are supplementary.
  12. Definition of Linear Pair-A linear pair is a pair of adjacent angles whose non common sides form a line.
  13. Definition of Vertical Angles- two nonadjacent angles formed by two intersecting lines.
  14. Vertical Angles Theorem- Vertical angles are congruent.
  15. Definition of Parallel lines- Parallel lines are lines that never intersect.
  16. Corresponding Angles Postulate- If the lines are parallel, then the corresponding angles are congruent.
  17. Converse: When corresponding angles are congruent, the lines are parallel.
  18. Alternate Interior Angles Theorem- If the lines are parallel, then the alternate interior angles are congruent.
  19. Converse: If the alternate interior angles are congruent, then the lines are parallel.
  20. Alternate Exterior Angles Theorem- If the lines are parallel, then the alternate exterior angles are congruent.
  21. Converse- If the alternate exterior angles are congruent, then the lines are parallel.
  22. Same Side Interior Angles Theorem- If the lines are parallel, then the SS Int angles are supplementary.
  23. Converse- If the SS Int angles are supplementary then the lines are parallel.
  24. Triangle Sum Theorem- All 3 angles add up to 180 degrees.
  25. 3rd Angles Theorem- If two pairs of angles are congruent between two triangles, then the third pair of angles must be congruent.
  26. Remote Angles- Two interior angles that are nonadjacent to a given exterior angle.
  27. Remote Angles Theorem- The measures of the two remote angles add up to the measure of the given exterior angle.
  28. SSS- Two triangles are congruent, if they have 3 pairs of congruent sides.
  29. SAS- Two triangles are congruent if they have two pairs of congruent sides, and the angles between those sides are also congruent.
  30. AAS- Two triangles are congruent if two angle pairs are congruent and a pair of sides are congruent, but not between the two congruent angles.
  31. ASA- Two triangles are congruent if two angle pairs are congruent and the sides between the two congruent angles are also congruent.
  32. CPCTC- Corresponding Parts of Congruent Triangles are Congruent.
  33. Definition of Isosceles Triangles- An isosceles triangle is a triangle with two congruent sides.
  34. Properties of Isosceles Triangles- The two base angles of an isosceles triangle are congruent.

 

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