Which biconditional statement is true?
a. a shape is a rectangle if and only if the shape has exactly four sides and four right angles.
b. a shape is a trapezoid if and only if the shape has a pair of parallel sides.
c. a shape is a triangle if and only if the shape has three sides and three acute angles.
d. a shape is a square if and only if the shape has exactly four congruent side

Answer;

A .a shape is a rectangle if and only if the shape has exactly four sides and four right angles.

Explanation;

-A rectangle is a 4-sided flat shape with straight sides where all interior angles are right angles (90°). Also opposite sides are parallel and of equal length. Example: A square is a special type of rectangle, here all the four sides are equal.

Therefore; the characteristics of a rectangle include;

-All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).

-All angles are right angles by definition.

-The diagonals are congruent.

synovial joints are characterized by the presence of a joint cavity. the walls of this space are formed by the articular capsule, a fibrous connective tissue structure that is attached to each bone just outside the area of the bone’s articulating surface. the bones of the joint articulate with each other within the joint cavity.

friction between the bones at a synovial joint is prevented by the presence of the articular cartilage, a thin layer of hyaline cartilage that covers the entire articulating surface of each bone. however, unlike at a cartilaginous joint, the articular cartilages of each bone are not continuous with each other. instead, the articular cartilage acts like a teflon® coating over the bone surface, allowing the articulating bones to move smoothly against each other without damaging the underlying bone tissue. lining the inner surface of the articular capsule is a thin synovial membrane. the cells of this membrane secrete synovial fluid (synovia = “a thick fluid”), a thick, slimy fluid that provides lubrication to further reduce friction between the bones of the joint. this fluid also provides nourishment to the articular cartilage, which does not contain blood vessels. the ability of the bones to move smoothly against each other within the joint cavity, and the freedom of joint movement this provides, means that each synovial joint is functionally classified as a diarthrosis.

outside of their articulating surfaces, the bones are connected together by ligaments, which are strong bands of fibrous connective tissue. these strengthen and support the joint by anchoring the bones together and preventing their separation. ligaments allow for normal movements at a joint, but limit the range of these motions, thus preventing excessive or abnormal joint movements. ligaments are classified based on their relationship to the fibrous articular capsule. an extrinsic ligament is located outside of the articular capsule, an intrinsic ligament is fused to or incorporated into the wall of the articular capsule, and an intracapsular ligament is located inside of the articular capsule.

at many synovial joints, additional support is provided by the muscles and their tendons that act across the joint. a tendon is the dense connective tissue structure that attaches a muscle to bone. as forces acting on a joint increase, the body will automatically increase the overall strength of contraction of the muscles crossing that joint, thus allowing the muscle and its tendon to serve as a “dynamic ligament” to resist forces and support the joint. this type of indirect support by muscles is very important at the shoulder joint, for example, where the ligaments are relatively weak.

additional structures associated with synovial joints

a few synovial joints of the body have a fibrocartilage structure located between the articulating bones. this is called an articular disc, which is generally small and oval-shaped, or a meniscus, which is larger and c-shaped. these structures can serve several functions, depending on the specific joint. in some places, an articular disc may act to strongly unite the bones of the joint to each other. examples of this include the articular discs found at the sternoclavicular joint or between the distal ends of the radius and ulna bones. at other synovial joints, the disc can provide shock absorption and cushioning between the bones, which is the function of each meniscus within the knee joint. finally, an articular disc can serve to smooth the movements between the articulating bones, as seen at the temporomandibular joint. some synovial joints also have a fat pad, which can serve as a cushion between the bones.