Rectangles, rhombuses, and also squares space parallelograms identified by their diagonals, angles, and sides.
You are watching: What is a parallelogram with four congruent sides
Rectangles, rhombuses (also dubbed rhombi) and squares room all more specific execution of parallelograms, also called distinct parallelograms.A square is a rectangle if and also only if it has four right (congruent) angles.
(ABCD) is a rectangle if and also only if (angle Acong angle Bcong angle Ccong angle D).A quadrilateral is a rhombus if and also only if it has four congruent sides.
(ABCD) is a rhombus if and also only if (overlineABcong overlineBC cong overlineCD cong overlineAD).A quadrilateral is a square if and only if that has four right angles and four congruent sides. Through definition, a square is a rectangle and also a rhombus.
(ABCD) is a square if and only if (angle Acong angle Bcong angle Ccong angle D) and (overlineABcong overlineBC cong overlineCD cong overlineAD).
You can always show that a parallelogram is a rectangle, rhombus, or square by utilizing the meanings of these shapes. There space some added ways to prove parallelograms space rectangles and also rhombuses, shown below:
1. A parallel is a rectangle if the diagonals room congruent.
(ABCD) is parallelogram. If (overlineACcong overlineBD), climate (ABCD) is likewise a rectangle.
2. A parallelogram is a rhombus if the diagonals space perpendicular.
For the an initial figure, every sides space congruent and one angle is (135^circ), therefore the angles are not congruent. This is a rhombus.
For the second figure, all four angles are congruent but the sides are not. This is a rectangle.
Is a rhombus SOMETIMES, ALWAYS, or never ever a square? define why.
A rhombus has four congruent sides and a square has four congruent sides and angles. Therefore, a rhombus is a square once it has congruent angles. This method a rhombus is occasionally a square.
List everything you know about the square (SQRE).
A square has actually all the nature of a parallelogram, rectangle and rhombus.
|(overlineSQparallel overlineER)||(overlineSQcong overlineERcong overlineSEcong overlineQR)||(mangle SER=mangle SQR=mangle QSE=mangle QRE=90^circ)|
|(overlineSEparallel overlineQR)||(overlineSRperp overlineQE)|
|(angle SEQcong angle QERcong angle SQEcong angle EQR)||(overlineSRcong overlineQE)|
|(angle QSRcong angle RSEcong angle QRScong angle SRE)||(overlineSAcong overlineARcong overlineQAcong overlineAE)|
All the bisected angles room (45^circ).
api/deki/files/1777/f-d_7b54067dac4c1495cfcbd0706ad44c840c577de994d607973c664859%252BIMAGE_TINY%252BIMAGE_TINY.png?revision=1&size=bestfit&width=450" /> figure (PageIndex23)
For concerns 16-19 identify if the adhering to are ALWAYS, SOMETIME, or never true. Define your reasoning.
See more: What Is Italian Parsley The Same As Flat Leaf Parsley And Italian Parsley?