Question

Can someone please help. Please show work

Answer 1

For parallelogram:

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

for rectangle:

A quadrilateral is a polygon in Euclidean plane geometry with four edges (sides) and four vertices (corners). Other names for quadrilateral include quadrangle (in analogy to triangle), tetragon (in analogy to pentagon and hexagon), and 4-gon (in analogy to n-gons for arbitrary values of n).

for rhombus:

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a diamond.

for Square:

·There are four methods that you can use to prove that a quadrilateral is a square. In the last three of these methods, you first have to prove (or be given) that the quadrilateral is a rectangle, rhombus, or both:

·If a quadrilateral has four congruent sides and four right angles, then it’s a square (reverse of the square definition).

·If two consecutive sides of a rectangle are congruent, then it’s a square (neither the reverse of the definition nor the converse of a property).

·If a rhombus contains a right angle, then it’s a square (neither the reverse of the definition nor the converse of a property).

·If a quadrilateral is both a rectangle and a rhombus, then it’s a square (neither the reverse of the definition nor the converse of a property).

Answer 2

Answer:

11. parallelogram, rectangle

12. parallelogram, rhombus

13. parallelogram, square