We included HMH Into Math Grade 5 Answer Key PDF Module 20 Lesson 3 Classify and Organize Quadrilaterals to make students experts in learning maths.

I Can classify and compare quadrilaterals.

Farmlands, when viewed from above, often look like they are divided into different polygons, including quadrilaterals. Look at the quadrilaterals shown. Make a list of five attributes that a quadrilateral can have. Then write the number of each quadrilateral matching each attribute. A triangle has three sides, three vertices, and three angles.
Number  11 is a triangle.

• a square is the only regular quadrilateral.
• all angles are equal.
• all sides are of equal length.
• opposite sides are parallel.
• the diagonals bisect each other at.
• the diagonals are equal in length.

The shapes matching the attributes are:
1, 2, 6, 7, 8 9, 12 , 10 these are the quadrilaterals that match the properties.

Turn and Talk
Compare your list with the list of a classmate. Based on your attributes, how would you classify quadrilaterals?
My friend classified according to the sides, vertices and angles
by that the numbers 9, 10, 12 are excluded in my friends attributes

Build Understanding

Question 1.
Some quadrilaterals can be classified by more than one attribute.
Connect to Vocabulary
A parallelogram is a quadrilateral with pairs of opposite sides that are congruent and parallel. Some parallelograms have special names based on their specific properties.
A rectangle is a parallelogram with four right angles.
A rhombus is a parallelogram with four congruent sides.
A square is a parallelogram with four congruent sides and four right angles.

A. Complete the chart.  B. What attributes does a square have in common with a rhombus?
In square the angles are right angles
But not in a rhombus
Square and rhombus have 4 sides 4 angles and 4 vertices
Square and rhombus have equal sides.

C. What attributes does a rectangle have in common with a parallelogram?
Their opposite sides are parallel
their diagonals bisect each other and divide the parallelogram into two congruent triangles,
and opposite sides and angles are congruent.

Turn and Talk What three figures have attributes in common? What are the attributes?
Rhombus , rectangle and square
these 3 shapes have 4 sides, angles and 4 vertices
these are the 3 attributes that are common for a Rhombus , rectangle and square

Step It Out

Question 2.
An artist draws a stained glass design using quadrilaterals.
Connect to Vocabulary
There are two accepted definitions of a trapezoid. One definition defines a trapezoid as having exactly one pair of parallel sides. The other definition defines a trapezoid as having at least one pair of parallel sides. A. Find and shade all the quadrilaterals among these figures in the diagram. a quadrilateral can be defined as a closed,
two-dimensional shape which has four straight sides.
The polygon has four vertices or corners.

B. Find the trapezoids.
Write 1 if there is exactly one pair of parallel sides. Explanation:
A trapezoid is a quadrilateral with one pair of opposite sides parallel.

Write 2 if there is at least one pair of parallel sides. Explanation:
Quadrilateral with one pair of parallel sides is a trapezoid.
If it has two pairs of parallel sides it is a parallelogram,
but parallelograms are also trapezoids.

C. Write 3 in each parallelogram. Explanation:
a quadrilateral with opposite sides parallel and equal.
Rhombus, square and rectangle and some trapezoids with 2 sides parallel are parallelograms.

D. Based on parts B and C, what attributes do parallelograms and trapezoids share under each definition of a trapezoid?
Rhombus, square and rectangle and some trapezoids with 2 sides parallel are parallelograms.
A trapezoid has at least one parallel side and a parallelogram has 2 sides parallel.

Check Understanding

Question 1.
Tonya defines a trapezoid as having exactly one pair of parallel sides. Which quadrilaterals are also always trapezoids by her definition? Explain.
Rhombus, square and rectangle and some trapezoids with 2 sides parallel are parallelograms.
A trapezoid has at least one parallel side and a parallelogram has 2 sides parallel.

Identify each statement as true or false.

Question 2.
A parallelogram is always a rhombus.
no
Explanation:
every rhombus is a parallelogram but not  A parallelogram is always a rhombus.
It can be a square or a rectangle or a trapezoid.

Question 3.
A rhombus is always a parallelogram.
Yes.
Explanation:
All rhombuses are parallelograms.
A parallelogram has opposite sides parallel and equal in length.
Here the opposite angles are equal.

Question 4.
A square is always a rhombus.
Yes
Explanation:
A square is always a rhombus since all the sides of a square are equal in length.
the diagonals of square and rhombus are perpendicular to each other and bisect the opposite angles.

Question 5.
A rectangle is always a rhombus.
No
Explanation:
a rectangle is not always a rhombus
A rectangle has two sets of congruent sides
whereas all four sides of a rhombus are congruent.

Question 6.
Use Structure Kent draws a quadrilateral that is a rhombus but not a square. What are its properties?
A rhombus is a quadrilateral with all sides equal in length.
A quadrilateral is a rhombus but not a square if the length of diagonals are not equal. Use Structure Classify the quadrilateral in as many ways as possible. Write quadrilateral, parallelogram, rectangle, rhombus, or square.

Question 7. Explanation:
Quadrilateral is a shape which has 4 sides and 4 angles.
no parallel sides.

Question 8. Parallelogram
Explanation:
a quadrilateral with opposite sides parallel and equal.
All the opposite sides are parallel.

Question 9. Square
Explanation:
A square has 4 sides and 4 angles, 4 vertices
A square is always a rhombus

• All four internal angles of a square are equal
• The central angle of a square is equal to 90°
• The external angle of a square is equal to 90°.
• The diagonals of a square are equal and bisect each other, meeting at 90°.

Question 10.
Attend to Precision Marylia says that a parallelogram is also a trapezoid. According to Marylia, what other shapes are also trapezoids? How do you know?
Yes, parallelogram is a Trapezoid.
Explanation:
Trapezoid is a shape which has at least one parallel sides
a trapezoid as a quadrilateral with exactly one pair of parallel sides
Rectangle, rhombus , square are also the some of examples

Question 11.
Open-Ended Patrick defines a trapezoid as a quadrilateral with exactly one pair of parallel sides. How can he draw a line segment on this figure to make a trapezoid? Draw the segment and explain.  Explanation:
when we drawn a line segment the opposite sides are not parallel
It has only one parallel sides.
When it is only one sides parallel then it is a trapezoid.
When we drawn a line the rectangle changed to a trapezoid.

I’m in a Learning Mindset!

What evidence do I have that I classified quadrilaterals correctly?