Question

PLEASE HELP!!!!

Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their angles. Which one(s) have angles whose sum is 360 degrees? Which one(s) have both pairs of opposite angles that are congruent? Which one(s) have four angles?

Answer 1

The square, rectangle, and rhombus are all considered parallelograms. Squares have four sides, four 90 degree angles, 2 pairs of opposite congruent angles (all the angles are congruent), the angles add up to a sum of 360 degrees. Rectangles have four sides, four 90 degree angles that add up to 360 degrees, 2 pairs of opposite congruent angles (all the angles are congruent). Rhombuses have four sides, four angles in total measuring up to 360 degrees no matter the combination of angles because the oposite angles are congruent (2 acute angles and two obtuse angles).

While the rhombus is the only shape within this trio to have a pair of congruent acute and a pair of congruent obtuse angles the square and rectangle both have 4 congruent angles. All 3 shapes have a sum of 360 degrees when the angles are added together, all 3 have pairs of opposite angles being congruent, and all 3 shapes have 4 angles in total.

Answer 2

This seems to be more of a middle-school-level of a geometry question vs college level.

Either way, what you're doing here is comparing 3 shapes. The square, rectangle, and rhombus. You should definitely know what a square and rectangle look like, but in case you don't know the rhombus, it's the shape that's usually allocated with diamonds, on a 2D plane.

All of these shapes are considered parallelograms. They all have similar features and characteristics, but only to some extent.

Square=Four sides, four 90 degree angles, 2 pairs of opposite congruent angles (meaning all angles are congruent in this case), sum of 360 degrees (90*4)

Rectangle=Four sides, four 90 degree angles, 2 pairs of opposite congruent angles (meaning all angles are congruent in this case), sum of 360 degrees (90*4)

Rhombus= Four sides, Four angles in total measuring up to 360 degrees, 2 acute angles (congruent; less than 90), two obtuse angles (congruent; more than 90). Angle measurements can fluctuate within the 2 acute-2 obtuse parameters. 2 pairs of opposite congruent angles, however, these are not all congruent with each other, unlike the previous two.

All 3 sum to 360 degrees
All 3 have both pairs of opposite angles congruent
All 3 have 4 angles.

~Hope this helps!