Proving Properties of Parallelogram

The quadrilateral formed by the angle bisectors of a parallelogram will be a ___________.

• Rectangle

• Square

• Rhombus

• Trapezium

Answer explanation

Given : ABCD is a parallelogram and AP, BR, CR, and DP be are the bisectors of ∠A, ∠B, ∠C and ∠D, respectively. Diagram To prove: Quadrilateral PQRS is a rectangle. Proof Since, ABCD is a parallelogram, then DC || AB and DA is a transversal. ∠A+∠D= 180° ---- sum of interior angles of a parallelogram is 180° ½ ∠A+ ½ ∠D = 90° ----- dividing both segs by 2 ∠PAD + ∠PDA = 90° ∠APD = 90° ----- since sum of all angles of a triangle is 180° ∴ ∠SPQ = 90° ------ vertically opposite angles ∠PQR = 90° ∠QRS = 90° and ∠PSR = 90° Thus, PQRS is a quadrilateral whose each angle is 90°. Hence, PQRS is a rectangle.

Tags

CCSS.HSG.CO.C.11

Consecutive angles of a parallelogram are supplementary

• sometimes true

• always true

• never true

Tags

CCSS.HSG.CO.C.11

What is the best definition of a parallelogram?

• quadrilateral with one pair of parallel sides 

• quadrilateral with two pairs of parallel sides

• any four sided figure with opposite sides congruent 

• a quadrilateral with two pairs of congruent sides

Tags

CCSS.2.G.A.1

All rectangles are parallelograms.

• True

• False

Tags

CCSS.HSG.CO.C.11

In the picture, side AB must be equal to which side?

• AE

• AD

• CD

• BC

Tags

CCSS.HSG.CO.C.11

The opposite angles of a parallelogram are ...

• complementary

• equal

• supplementary

• perpendicular

Tags

CCSS.HSG.C.A.3

In a parallelogram, consecutive angles are __________.

• congruent

• supplementary

• corresponding

• parallel

Tags

CCSS.HSG.CO.C.11

In a parallelogram, diagonals are __________.

• perpendicular

• bisected

• congruent

• parallel

Tags

CCSS.HSG.CO.C.11

Which is NOT a property of a parallelogram?

• Diagonals bisect each other

• Diagonals are equal

• Both pairs of opposite sides are parallel

• Both pairs of opposite angles are congruent

Tags

CCSS.HSG.CO.C.11

The opposite sides of a parallelogram are equal.

• true

• false

• maybe

• sometimes

Tags

CCSS.HSG.CO.C.11