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.

## HMH Into Math Grade 5 Module 20 Lesson 3 Answer Key Classify and Organize Quadrilaterals

I Can classify and compare quadrilaterals.

**Spark Your Learning**

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.

Answer:

A triangle has three sides, three vertices, and three angles.

Number 11 is a triangle.

**Properties of quadrilaterals**

- 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?

Answer:

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.

Answer:

B. What attributes does a square have in common with a rhombus?

Answer:

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?

Answer:

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?

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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?

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

**On Your Own**

Question 6.

**Use Structure** Kent draws a quadrilateral that is a rhombus but not a square. What are its properties?

Answer:

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.

Answer:

Quadrilateral

Explanation:

Quadrilateral is a shape which has 4 sides and 4 angles.

no parallel sides.

Question 8.

Answer:

Parallelogram

Explanation:

a quadrilateral with opposite sides parallel and equal.

All the opposite sides are parallel.

Question 9.

Answer:

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?

Answer:

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.

Answer:

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?

Answer:

quadrilaterals are parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid.

A rhombus is a parallelogram with four congruent sides.

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

A quadrilateral is a polygon with four sides.

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals.