Math Problem Statement

Which of the following must be a square? A. A figure that is both a rhombus and a rectangle B. A figure that is both a rectangle and a trapezoid C. A figure that is both a rectangle and a parallelogram D. A figure that is both a rhombus and a parallelogram

Solution

The questionThe asks question is which asking figure ** whichmust figure be must be a a square square**. Let's analyze the based options on the given properties.

:

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Let's ** analyzeOption A: each A option figure:

that1 is both. a Option A: rhomb Aus and figure a that rectangle is. both a rhombus

  • and A square a is defined as rectangle a** figure
    that - is A ** both arh rhombombusus has all ( four sidesall of sides equal) equal and a length.
    rectangle (all - angles equal A ** torectangle ** has90° all angles equal)**.
    to ( 90 -^\circ Therefore, this \ option).
  • If a figure is correctly describes a square.
  1. ** bothOption a B rhomb: Aus figure ** thatand** is a both a rectangle rectangle, and it a must trapezo satisfy:id.
    ** -
    All sides - are A rectangle equal ( doesrh notomb necessarilyus have property). all sides
    equal , - and All a angles trape arezo ( 90^\circid only has \ one pair of parallel) sides (.rectangle
    property ).
  • This does - This not combination define makes a the square.

figure a3. ** squareOption C.:
A ✅ figure ** thatOption is both A is a rectangle correct and** a.

2 parallelog. Option Bram.: A figure that

  • All is rectangles both are a paralle rectanglelogr and aams trape, butzoid rectangles do** not
    necessarily have - A all rectangle sides has equal. two
    pairs of parallel sides -, This does not while a trapezoid guarantee a has square.
  1. only ** one pairOption of D: parallel sides A. figure
    that is both - a A figure rh cannotomb beus both and a a paralle rectangle andlogram a. trapezo
    id simultaneously -. A
    rh ombus ❌ is ** aThis is paralle incorrectlogram
    ,.

but3 it. does ** notOption C require: all angles A to figure be that is90 both°. a
rectangle and - a This paralle islog notram necessarily** a
square .

-### **Correct Answer All: rectangles are A parallelogr.ams by A figure definition that, is but not both a all rh paralleomblogrus andams a are rectangle squares..
**


Would - you This like condition a alone further does breakdown not of square guarantee properties a or square related. concepts
? Here are some additional ❌ related questions:

1.This What is are incorrect.

4 the. properties Option D: of A a figure square that? is
both2 a. rh Howomb isus a and square a different paralle fromlog aram
rh
ombus and - a All rectangle rhomb?
uses3 are. paralle Whylog isr everyams, square a but paralle notlog allram rh?omb
uses4 are. squares Can. a
rectangle be - a This square condition? alone Under does what not conditions?
guarantee5 a square..
How do you ❌ prove This that is a incorrect given quadr.

ilateral is---

a square Final?

Answer**:Tip **:A. To prove A figure a that figure is is both a a square rh,omb youus must and a show that rectangle all sides

areWould equal you like and further clarification or details?

all angles are---

###90 Related°. Questions:

  1. What are the defining properties of a square?
  2. How is a rhombus different from a square?
  3. What is the relationship between rectangles and parallelograms?
  4. Can a trapezoid ever be classified as a parallelogram?
  5. What are the key differences between a square and a rhombus?

Tip:

Always check if the figure satisfies all properties of a square:

  • Four equal sides.
  • Four 9090^\circ angles.

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Math Problem Analysis

Mathematical Concepts

Properties of Squares
Properties of Rectangles
Properties of Rhombuses
Parallelograms
Quadrilaterals

Formulas

Definition of a Square: Four equal sides and four right angles

Theorems

A square is both a rhombus (all sides equal) and a rectangle (all angles 90°).

Suitable Grade Level

Grades 7-9