Common Core Geometry Proofs

HSG.CO Prove Geometric Theorems

*SS denotes a blank student sheet

HSG.CO.C.9 Prove theorems about lines and angles

• Vertical angles are congruent (SS)
  
• When a transversal crosses parallel lines, alternate interior angles are congruent (SS)
  
• When a transversal crosses parallel lines, corresponding angles are congruent (SS)
  
• Points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints (SS)

HSG.CO.C.10 Prove theorems about triangles

• Measures of interior angles of a triangle sum to 180° (SS)
  
• Base angles of isosceles triangles are congruent (SS)
  
• The segment joining midpoints of two sides of a triangle is parallel to the third side and half the length (SS)

HSG.CO.C.11 Prove theorems about parallelograms

• Opposite sides are congruent (SS)
• Opposite angles are congruent (SS)
• The diagonals of a parallelogram bisect each other (SS)
  •  and conversely (SS)
• Rectangles are parallelograms with congruent diagonals (SS)