Quadrilaterals with corresponding sides of equal length are (sometimes, always, never) congruent
Ans. Always
Well, isn't that convenient? So if you have two quadrilaterals with corresponding sides of equal length, then you can confidently say that they are always congruent. No need to measure those sides over and over again. Just trust that the lengths are the same and enjoy the congruency party! Just make sure to bring some congruent snacks.
Quadrilaterals with corresponding sides of equal length are always congruent.
To determine whether quadrilaterals with corresponding sides of equal length are congruent, we need to understand what congruence means in geometry. Two figures are said to be congruent if they have the same shape and size. Essentially, this means that all corresponding sides and angles of the two figures are equal.
Now, let's consider quadrilaterals. A quadrilateral is a polygon with four sides. If we have two quadrilaterals where all the corresponding sides are equal in length, it means that the lengths of their sides match up perfectly. In this case, it is always true that the two quadrilaterals are congruent.
To prove this, we can use the concept of SSS (Side-Side-Side) congruence, which states that if the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. This concept applies to quadrilaterals as well.
So, if all the corresponding sides of two quadrilaterals are equal, we can pair each side of one quadrilateral with its corresponding side in the other quadrilateral, apply the SSS congruence principle, and conclude that the two quadrilaterals are congruent.
In summary, when quadrilaterals have corresponding sides of equal length, they are always congruent.
nope
consider a rectangle, with sides of width 4 cm and length 10 cm.
I can also draw a parallelogram with opposite pair of sides of 4 and 10 cm.
they are not congruent.
I would go with "sometimes"