A square and a parallelogram are both convex quadrilaterals. And that is where their similarities lie. They have far more differences than similarities. Here they are listed out.
Square. Its properties are
(a) All sides are equal.
(b) Opposite sides are equal and parallel.
(c) All angles are equal to 90 degrees.
(d) The diagonals are equal.
(e) Diagonals bisect each other at right angles.
(f) Diagonals bisect the angles.
(g) The intersection of the diagonals is the circumcentre. That is, you can draw a circle with that as centre to pass through the four corners.
(h) The intersection of the diagonals is also the incentre. That is, you can draw a circle with that as centre to touch all the four sides.
(i) Any two adjacent angles add up to 180 degrees.
(j) Each diagonal divides the square into two congruent isosceles right-angled triangles.
(k) The sum of the four exterior angles is 4 right angles.
(l) The sum of the four interior angles is 4 right angles.
(m) Lines joining the mid points of the sides of a square in an order form another square of area half that of the original square.
(n) If through the point of intersection of the two diagonals you draw lines parallel to the sides, you get 4 congruent squares each of whose area will be one-fourth that of the original square.
(o) Join the quarter points of a diagonal to the vertices on either side of the diagonal and you get a rhombus of half the area of the original square.
(p) Revolve a square about one side as the axis of rotation and you get a cylinder whose diameter is twice the height.
(q) Revolve a square about a line joining the midpoints of opposite sides as the axis of rotation and you get a cylinder whose diameter is the same as the height.
(r) Revolve a square about a diagonal as the axis of rotation and you get a double cone attached to the base whose maximum diameter is the same as the height of the double cone.
Parallelogram. Its properties are
(a) Opposite sides are equal and parallel.
(b) Opposite angles are equal.
(c) Diagonals bisect each other.
(d) The diagonals bisect the parallelogram into two congruent triangles.
(e) Any two adjacent angles add up to 180 degrees.
(f) The angle bisectors of the opposite angles of a parallelogram are parallel.
(g) The angles bisectors of two adjacent angles form a right angle where they meet.
(h) ) The angle bisectors of all the 4 angles form a rectangle inside the parallelogram.
(i) The sum of the four exterior angles is 4 right angles.
(j) The sum of the four interior angles is 4 right angles.
(k) Join the midpoints of the four sides in order and you get another parallelogram.
(l) Revolve a parallelogram about the longer side as the axis of rotation and you get a cylindrical surface with a convex cone at one end a concave cone at the other end. Their slant heights will be the same as the shorter sides of the parallelogram.
(m) Revolve a parallelogram about the shorter side as the axis of rotation and you get a cylindrical surface with a convex cone at one end a concave cone at the other end. Their slant heights will be the same as the longer sides of the parallelogram.
(n) Revolve a parallelogram about a line joining the midpoints of opposite longer sides as the axis of rotation and you get a cylindrical surface with concave cones at the both ends.
(o) Revolve a parallelogram about a line joining the midpoints of opposite shorter sides as the axis of rotation and you get a cylindrical surface with concave cones at the both ends.
(p) Revolve a parallelogram about the longer diagonal as the axis of rotation and you get a solid with two cones at the ends of the axis with the slant heights same as the width of the rectangle separated by two frustums of cones attached at their smaller ends.
(q) Revolve a parallelogram about the shorter diagonal as the axis of rotation and you get a solid with two frustums of cones attached at their smaller ends.
(r) The larger obtuse angles formed by the diagonals where they intersect are opposite the longer sides of the parallelogram and the smaller acute angles are opposite the shorter sides of the parallelogram.
Answers & Comments
Answer:
Yes Bc..
Step-by-step explanation:
A square and a parallelogram are both convex quadrilaterals. And that is where their similarities lie. They have far more differences than similarities. Here they are listed out.
Square. Its properties are
(a) All sides are equal.
(b) Opposite sides are equal and parallel.
(c) All angles are equal to 90 degrees.
(d) The diagonals are equal.
(e) Diagonals bisect each other at right angles.
(f) Diagonals bisect the angles.
(g) The intersection of the diagonals is the circumcentre. That is, you can draw a circle with that as centre to pass through the four corners.
(h) The intersection of the diagonals is also the incentre. That is, you can draw a circle with that as centre to touch all the four sides.
(i) Any two adjacent angles add up to 180 degrees.
(j) Each diagonal divides the square into two congruent isosceles right-angled triangles.
(k) The sum of the four exterior angles is 4 right angles.
(l) The sum of the four interior angles is 4 right angles.
(m) Lines joining the mid points of the sides of a square in an order form another square of area half that of the original square.
(n) If through the point of intersection of the two diagonals you draw lines parallel to the sides, you get 4 congruent squares each of whose area will be one-fourth that of the original square.
(o) Join the quarter points of a diagonal to the vertices on either side of the diagonal and you get a rhombus of half the area of the original square.
(p) Revolve a square about one side as the axis of rotation and you get a cylinder whose diameter is twice the height.
(q) Revolve a square about a line joining the midpoints of opposite sides as the axis of rotation and you get a cylinder whose diameter is the same as the height.
(r) Revolve a square about a diagonal as the axis of rotation and you get a double cone attached to the base whose maximum diameter is the same as the height of the double cone.
Parallelogram. Its properties are
(a) Opposite sides are equal and parallel.
(b) Opposite angles are equal.
(c) Diagonals bisect each other.
(d) The diagonals bisect the parallelogram into two congruent triangles.
(e) Any two adjacent angles add up to 180 degrees.
(f) The angle bisectors of the opposite angles of a parallelogram are parallel.
(g) The angles bisectors of two adjacent angles form a right angle where they meet.
(h) ) The angle bisectors of all the 4 angles form a rectangle inside the parallelogram.
(i) The sum of the four exterior angles is 4 right angles.
(j) The sum of the four interior angles is 4 right angles.
(k) Join the midpoints of the four sides in order and you get another parallelogram.
(l) Revolve a parallelogram about the longer side as the axis of rotation and you get a cylindrical surface with a convex cone at one end a concave cone at the other end. Their slant heights will be the same as the shorter sides of the parallelogram.
(m) Revolve a parallelogram about the shorter side as the axis of rotation and you get a cylindrical surface with a convex cone at one end a concave cone at the other end. Their slant heights will be the same as the longer sides of the parallelogram.
(n) Revolve a parallelogram about a line joining the midpoints of opposite longer sides as the axis of rotation and you get a cylindrical surface with concave cones at the both ends.
(o) Revolve a parallelogram about a line joining the midpoints of opposite shorter sides as the axis of rotation and you get a cylindrical surface with concave cones at the both ends.
(p) Revolve a parallelogram about the longer diagonal as the axis of rotation and you get a solid with two cones at the ends of the axis with the slant heights same as the width of the rectangle separated by two frustums of cones attached at their smaller ends.
(q) Revolve a parallelogram about the shorter diagonal as the axis of rotation and you get a solid with two frustums of cones attached at their smaller ends.
(r) The larger obtuse angles formed by the diagonals where they intersect are opposite the longer sides of the parallelogram and the smaller acute angles are opposite the shorter sides of the parallelogram.