Proving A Quadrilateral Is A Parallelogram Worksheet For this we must use the converses of our precious theorems Theorem If a quadrilateral is a parallelogram then its opposite sides are congruent If a quadrilateral is a parallelogram then its diagonals bisect each other If a quadrilateral is a parallelogram then its opposite angles are congruent Converse
Quadrilaterals that are Parallelograms Recall that a parallelogram is a quadrilateral with two pairs of parallel sides Even if a quadrilateral is not marked with having two pairs of sides it still might be a parallelogram The following is a list of theorems that will help you decide if a quadrilateral is a parallelogram or not 1 ID A 2 6 ANS Because diagonals NR and BO bisect each other NX RX and BX OX BXN and OXR are congruent vertical angles Therefore BNX ORX by SAS REF 080731b 7 ANS Parallelogram ANDR with AW and DE bisecting NWD and REA at points W and E Given AN RD AR DN Opposite sides of a parallelogram are congruent AE 1 2 AR WD 1 2 DN so AE WD Definition
Proving A Quadrilateral Is A Parallelogram Worksheet
Proving A Quadrilateral Is A Parallelogram Worksheet
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There are 5 basic ways to prove a quadrilateral is a parallelogram They are as follows Proving opposite sides are congruent Proving opposite sides are parallel Proving the quadrilateral s diagonals bisect each other Proving opposite angles are congruent Proving consecutive angles are supplementary adding to 180 If a quadrilateral meets any of the 5 criteria below then it must be a parallelogram Criteria proving a quadrilateral is parallelogram 1 If a quadrilateral has one pair of sides that are both parallel and congruent 2 If all opposite sides of the quadrilateral are congruent 3 Both pairs of opposite sides are parallel
Proving Quadrilaterals Are Parallelograms quadrilaterals Most of the work we did was computation based because we were already given the fact that the figures were parallelograms In this section proofs for parallelograms We can apply much of what we learned in the previous organized in our arguments Draw a picture of each quadrilateral to determine if it is a parallelogram by one of the following reasons Be able to explain your selection a Opposite sides congruent b Opposite angles congruent c Diagonals bisect each other d One pair of opposite sides is both parallel and congruent e Both pairs of opposite sides are parallel
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Theorem 2 A quadrilateral is a parallelogram if both pairs of opposite angles are congruent Image 5 Theorem 2 If and then the quadrilateral is a parallelogram Theorem 3 A A quadrilateral is any two dimensional flat shape having four sides A parallelogram on the other hand is a quadrilateral having two pairs of opposite parallel sides To prove whether a given quadrilateral is a parallelogram there are six possible ways Depending upon the information provided you need to use any one of the below given properties
If both pairs of opposite angles 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 Students are then asked to determine whether given quadrilaterals are parallelograms based on these concepts as well as solve problems Free Geometry Worksheet Proving that a Quadrilateral is a Parallelogram The definition of a parallelogram gives one way to prove that a quadrilateral is a parallelogram show both pair of opposite sides are parallel Complete the following theorems which provide four more ways 1 If both pairs of opposite sides of a quadrilateral are
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Proving A Quadrilateral Is A Parallelogram Worksheet - Draw a picture of each quadrilateral to determine if it is a parallelogram by one of the following reasons Be able to explain your selection a Opposite sides congruent b Opposite angles congruent c Diagonals bisect each other d One pair of opposite sides is both parallel and congruent e Both pairs of opposite sides are parallel