# By: Tyler Register and Tre Burse

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By: Tyler Register and Tre Burse
without 4.7 Proving quadrilateral properties Conditions for special quadrilaterals Constructing transformations By: Tyler Register and Tre Burse geometry

The Vocabulary and Theorems
A diagonal of a parallelogram divides the parallelogram into two equal triangles Opposite sides of a parallelogram are congruent Opposite angles of a parallelogram are congruent Diagonals of a parallelogram bisect each other

Theorems cont. A rhombus is a parallelogram
A rectangle is a parallelogram The diagonals and sides of a rhombus form 4 congruent triangles The diagonals of a rhombus are perpendicular The diagonals of a rectangle are congruent A square is a rhombus

Theorems cont. The diagonals of a square are perpendicular and are bisectors of the angles If two pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram

Theorems If one angle of a parallelogram is a right angle then the parallelogram is a rectangle If the diagonals of a parallelogram are congruent then the parallelogram is a rectangle If one pair of adjacent sides of a quadrilateral are congruent then the quadrilateral is a rhombus

More Theorems If the diagonals of a parallelogram bisect the angles of the parallelogram then it is a rhombus If the diagonals of a parallelogram are perpendicular than it is a rhombus Triangle mid-segment theorem- A mid-segment of a triangle is parallel to a side of the triangle and its length is equal to half the length of than side

The Last Theorem Slide Betweenness postulate- given the three points: P, Q, and R PQ+QR=PR then Q is between P and R on a line. The Triangle inequality theorem- The sum of any two sides of a triangle are greater than the other side.

4-5 Statements Reasons PLGM is a parallelogram and LM is a diagonal Given Def of parallelogram Objective- Prove quadrilateral conjectures by using triangle congruence postulates and theorems. PL II GM Given: parallelogram PLGM with diagonal LM < 3 = < 2 Alt. Int. angles PM II GL Def of parallelogram Prove: triangle LGM= triangle MPL <1 = <4 Alt. Int. angles LM=LM reflexive LGM= MPL ASA P L M G