Q2 ORAL: Geometric Properties in Writing Proofs

• 1. Betweenness: If B is between AC, then AC. = AB + BC.
• 2. Midpoint: If B is the midpoint of AC, then AB = BC.
• 3. Segment Bisector: If a line, ray or another segment bisects the segment AB at X, then AX ≅ BX.
• 4. Right Angle: If ∠A is a right angle, then m∠A = go°
• 5. Acute Angle: If ∠A is an acute angle, then m∠A < go°.
• 6. Obstuse Angle: If ∠A is an obtuse angle, then m∠A > go°.
• 7. Perpendicular Line Segments: If AB ⊥ AC, then ∠BAC is a right angle.
• 8. Complementary Angles: If ∠A and ∠B are complementary angles, then m∠A + m∠B = go°.
• 9. Supplementary Angles: If ∠A and ∠B are supplementary angles, then m∠A + m∠B = 180°.
• 10. Linear Pair: If two angles are adjacent such that two of the rays are opposite, then they form a linear pair.
• 11. Angle Bisector: If AD -> bisects ∠BAC, then ∠BAD ≅ ∠DAC.
• 12. Congruent Segments: If AB ≅ CD, then AB = CD.
• 13. Congruent Angles: If ∠A ≅ ∠B, then m∠A = m<B.
• 14. Supplement Postulate (SP): If two angles form a linear pair, then they are supplementary.
• 15. Vertical Angle Theorem (VAT): The measures of vertical angles are equal or vertical angles are congruent.
• 16. Angle Sum of a Point Postulate (ASPP): The sum of the measures of the angles at a point is 360.
• 17. Supplement Theorem (ST): Supplements of congruent angles are congruent.
• 18. Complement Theorem (CP): Complements of congruent angles are congruent.
• 19. PCAC Postulate: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
• 20. PAIC Theorem: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
• 21. PAEC Theorem: If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
• 22. PSSIAS Theorem: If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
• 23. Triangle Interior Angle Theorem (TIAT): The sum of the degree measures of the angles of a triangle is 180.
• 24. Third Angles Theorem: If two angles of one triangle are congruent to two angles of another, then the third angles are congruent.
• 25. Exterior Angles Theorem (EAT): The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
• 26. Quadrilateral Interior Angle Theorem (QIAT): The sum of the measures of the angles of a convex quadrilateral is 360.
• 27. Polygon Interior Angle Theorem (PIAT): The sum of the measures of the angles of a convex polygon with n sides is (n-2) 180.
• 28. Regular Polygon Interior Angle Theorem (RPIA): The measure of each angle of a regular n-gon is$(n-2)180/2$.
• 29. Polygon Exterior Angles Theorem (PEAT): The sum of the measures of the exterior angles, one at each vertex, of any convex polygon is 360.
• 30. Right Angles Congruency Theorem: Any two right angles are congruent.