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Transcript
Vertical Angle Theorem When 2 angles are formed by intersecting lines then they are congruent Angles across from each other are equal 1 2 1 2 Reflexive Property AB AB D Everything is equal to itself DF DF G F E Definition of Midpoint A midpoint divides a segment into two equal parts Every midpoint makes 2 congruent lines H I J K J is the midpoint of HL SO HJ JL L Alternate Interior Angles Theorem When a line cuts through 2 parallel lines the 2 alternate interior angles are congruent The opposite angles are equal andKL are parallel SO H I HI I K J K L H L Triangle Congruence Postulates The 5 properties used to determine if triangles are congruent SSS SAS AAS ASA HL NOT SSA Side – Side - Side When 2 triangles have all 3 corresponding sides congruent D A B C E CAB FDE by SSS F Side – Angle - Side 2 triangles are congruent when 2 corresponding sides and the inscribed angle are congruent The angle is in-between the 2 sides. H I by SAS J K HJI LJK L Angle – Side – Angle 2 triangles are congruent when 2 corresponding angles and the inscribed side are congruent The side is in – between the two angles X Y YXZ KJL Z J K L by ASA Angle – Angle – Side 2 triangles are congruent when 2 corresponding angles and the noninscribed side are congruent The side is NOT IN – BETWEEN the angles D DFG DFE by AAS G F E Hypotenuse – Leg Two RIGHT triangles are congruent when the hypotenuse and any corresponding leg are congruent ~ Only for RIGHT Triangles ~Only need 2 parts not 3 (hypotenuse+any other side) L M O N LOM NMO by HL 2 – Column Proofs A method used to prove a geometric idea using “Statement” and “Reason” columns A formal way to prove triangle congruence Statement Reason 1. 1. Given 2. 2. Parallelogram A quadrilateral with opposite sides parallel 1. Opposite sides congruent 2. Opposite angles congruent 3. Adjacent angles supplementary (add to 180) 4. Diagonals bisect (cut in half) Rhombus A Parallelogram with all sides congruent 1. Diagonals make right angles Rectangle A Parallelogram with all angles congruent (right angles) 1. Diagonals are congruent Square A parallelogram with all equal sides and equal angles (a rhombus AND a square) 1. Congruent diagonals 2. Perpendicular diagonals Trapezoid A quadrilateral with only 1 pair of parallel sides 1. Adjacent angles (between parallel sides) are supplementary Isosceles Trapezoid A trapezoid with 1 pair (legs) of congruent sides 1. Base angles congruent 2. Diagonals congruent Kite A quadrilateral with NO parallel sides 1. Diagonals perpendicular 2. Adjacent sides congruent 3. 1 pair of congruent angles (in between noncongruent sides)
