All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 12 Lesson 5 Classify Quadrilaterals will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 12 Lesson 5 Classify Quadrilaterals
You can classify quadrilaterals using one or more of the following attributes like congruent sides, parallel sides, and right angles.
Math in My World
Example 1
Trina cut out polygon mats to use for her travel photos. Use the figures below to determine the missing attribute(s) of each type of quadrilateral.
A square has all the attributes of a rectangle and a ______________.
Answer:
A square has all the attributes of a rectangle and a rhombus.
Explanation: A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal in length).
Example 2
One side of the Realia building in Madrid, Spain, is shown at the right Describe the attributes of the quadrilateral. Then classify it based on its attributes.
The quadrilateral has opposite sides ______________ and ______________.
So,it is a ______________.
Answer:
The quadrilateral has opposite sides that are congruent and parallel
so it is a rectangle.
In parallelogram also opposite sides are congruent and parallel.
Guided Practice
Question 1.
Describe the attributes of the quadrilateral below. Then classify the quadrilateral based on its attributes.
The opposite sides of the quadrilateral are ______________ and ______________.
There are ______________ right angles.
So, the quadrilateral is a _____________.
Answer:
The above-given quadrilateral:
The opposite sides of the quadrilateral are parallel and congruent.
There are 4 right angles.
so, the quadrilateral is a rectangle.
Properties of the rectangle:
– It has four sides and four vertices
– Each vertex has an angle equal to 90 degrees
– The opposite sides are equal and parallel
– Diagonal bisect each other
– The perimeter is equal to twice of the sum of its length and breadth
– The area is equal to the product of its length and breadth
– It’s a parallelogram with four right angles.
– Sum of all interior angles equal to 360 degrees
Question 2.
The design below is made up of a repeating quadrilateral. Describe the attributes of the quadrilateral. Then classify the quadrilateral based on its attributes.
The quadrilateral has _______________ congruent sides.
Opposite sides are _____________.
So, the quadrilateral is a _______________.
Answer:
The quadrilateral has 4 congruent sides.
Opposite sides are parallel
Therefore, the quadrilateral is a rhombus.
Talk Math
Tell why a square is a special kind of rectangle.
Answer:
Yes, a square is a special type of rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has:
– interior angles which measure 90∘ each.
– opposite sides that are parallel and equal.
– two diagonals that bisect each other and are equal.
* A square is called a special kind of rectangle because it possesses some additional properties which do not apply to rectangles. They are:
– All four sides of a square are equal.
– Diagonals of a square bisect each at right angles.
Independent Practice
Describe the attributes of each quadrilateral. Then classify the quadrilateral.
Question 3.
Answer:
The quadrilateral is parallelogram.
The four most important attributes of a parallelogram are:
– The opposite sides of a parallelogram are equal in measurement and they are parallel to each other.
– The opposite angles of a parallelogram are equal.
– The sum of interior angles of a parallelogram is equal to 360°.
– The consecutive angles of a parallelogram should be supplementary (180°).
Question 4.
Answer:
The quadrilateral is rhombus.
some of the attributes of the rhombus:
– All sides of the rhombus are equal.
– The opposite sides of a rhombus are parallel.
– Opposite angles of a rhombus are equal.
– In a rhombus, diagonals bisect each other at right angles.
– Diagonals bisect the angles of a rhombus.
– The sum of two adjacent angles is equal to 180 degrees.
Question 5.
Circle the quadrilateral(s) that have all the attributes of a parallelogram.
rectangle
rhombus
square
trapezoid
Answer:
Explanation:
A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent. Hence, a parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal. Observe the following figure which shows the three types of parallelograms:
Question 6.
Circle the quadrilateral(s) that have all the attributes of a rhombus.
rectangle
square
trapezoid
parallelogram
Answer:
Explanation:
A Square is a rhombus because like a rhombus, all the sides of a square are equal in length. Even, the diagonals of both square and rhombus are perpendicular to each other and bisect the opposite angles. Therefore, we can say the square is a rhombus.
State whether the following statements are true or false. If false, explain why.
Question 7.
All parallelograms have opposite sides congruent and parallel. Since rectangles are parallelograms, all rectangles have opposite sides congruent and parallel.
Answer: True
The vertices join the adjacent sides at 90° angles, which means the opposite sides of the rectangle are parallel lines. Since it has two sets of parallel sides and two pairs of opposite sides that are congruent, a rectangle has all of the properties of a parallelogram. That’s why a rectangle is always a parallelogram.
Question 8.
All squares have four congruent sides. Since rectangles are squares, all rectangles have four congruent sides.
Answer: False
All squares have four congruent sides. Rectangles are not squares. This is because rectangles do not have all congruent sides equal. In rectangles, opposite sides are equal.
Problem Solving
Question 9.
Mathematical PRACTICE Identify Structure Many aircraft display the shape of the American flag as shown below to indicate motion. Classify the quadrilateral.
Answer:
The above-given structure is a parallelogram.
A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent. Hence, a parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.
* Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.
Question 10.
Adena used a quadrilateral in her art design. The quadrilateral has no sides congruent and only one pair of opposite sides parallel. Classify the shape of the quadrilateral she used.
Answer:
The above-given:
One pair of opposite sides are parallel which is nothing but a trapezium.
A trapezoid also known as a trapezium is a four-sided polygon or a quadrilateral It has one set of opposite sides which are parallel and a set of non-parallel sides. The parallel sides are known as the bases and the non-parallel sides are known as the legs of the trapezoid.
Question 11.
Traci planted two tomato gardens. One garden is rectangular. The shape of the second garden has all the attributes of a rectangular garden. In addition, it has four congruent sides. Classify the shape of the second tomato garden.
Answer: square
Explanation:
The above-given:
The number of tomato gardens = 2
The shape of one garden is a rectangle.
The shape of the other gardens: A hint is given in the question.
Hint: all four sides are congruent
The quadrilateral having four sides equal is a square.
The garden is quadrilateral with 4 right angles and 4 congruent sides.
HOT Problems
Question 12.
Mathematical PRACTICE Model Math Draw a parallelogram that is neither a square, rhombus, nor rectangle.
Answer:
A parallelogram is a two-dimensional shape. It is a special case of quadrilaterals where both pairs of opposite sides are parallel and equal in length as shown in the image.
– The opposite sides are equal in length.
– The opposite angles are equal.
– The consecutive angles of a parallelogram are supplementary to each other.
– The diagonals of a parallelogram bisect each other.
– The diagonals divide a parallelogram into two triangles that are congruent to each other.
Question 13.
Building on the Essential Question How do I classify quadrilaterals using their attributes?
Answer:
We can classify quadrilaterals using attributes such as congruent sides, parallel sides, and right angles.
– A quadrilateral is a trapezoid or a trapezium if 2 of its sides are parallel to each other.
– A quadrilateral is a parallelogram if 2 pairs of sides parallel to each other.
– Squares and Rectangles are special types of parallelograms. Below are some special properties.– All internal angles are of “right angle” (90 degrees).– Each figure contains 4 right angles.– Sides of a square are of the same length (all sides are congruent) – Opposite sides of a rectangle are the same.– Opposite sides of a rectangle and square are parallel.
– A quadrilateral is a rhombus if all the sides are of equal length-specified 2 pairs of sides are parallel to each other.
– A kite is a special sort of quadrilateral, in which 2 pairs of adjacent sides are equal to each other.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 5 My Homework Answer Key
Practice
Describe the attributes of each quadrilateral. Then classify the quadrilateral.
Question 1.
Answer:
The quadrilateral is a trapezium.
Every quadrilateral has its own properties which make it identifiable and different from the rest. These properties give more insights into the geometrical construction of a shape. The properties of a trapezium are listed below:
– It is a 2D shape.
– The bases of a trapezium are parallel to each other.
– The length of both diagonals is equal.
– The diagonals of a trapezium always intersect each other.
– The adjacent interior angles sum up to 180°.
– The sum of all the interior angles in a trapezium is always 360°.
Question 2.
Answer:
– A quadrilateral is a rectangle.
– Each interior angle is 90 degrees and the opposite sides are parallel and equal to each other.
– The sum of all the interior angles is equal to 360 degrees
– The diagonals are parallel to each other and have the same length.
Question 3.
Circle the quadrilateral(s) that have all the attributes of a rectangle.
trapezoid
parallelogram
square
rhombus
Answer:
A square also fits the definition of a rectangle (all angles are 90°).
Problem Solving
Name all the quadrilaterals that have the given attributes.
Question 4.
opposite sides parallel _____________
Answer:
The quadrilaterals that are on opposite sides are parallel: parallelogram, rectangle, square, rhombus
Parallelogram: A parallelogram is a two-dimensional shape. It is a special case of quadrilaterals where both pairs of opposite sides are parallel and equal in length
rectangle: opposite sides are equal.
square: all sides are equal and parallel.
rhombus: It 4 congruent sides. The opposite sides are parallel.
Question 5.
four right angles _______________
Answer: square, rectangle
Explanation:
Rectangle:
– It has four sides and four vertices
– Each vertex has an angle equal to 90 degrees
– The opposite sides are equal and parallel
– Diagonal bisect each other
square:
– It has four sides and four vertices
– Each vertex has an angle equal to 90 degrees
– The sides are equal and parallel
Question 6.
exactly one pair of opposite sides parallel ________________
Answer:
One pair of opposite sides are parallel which is nothing but a trapezium.
A trapezoid also known as a trapezium is a four-sided polygon or a quadrilateral It has one set of opposite sides which are parallel and a set of non-parallel sides. The parallel sides are known as the bases and the non-parallel sides are known as the legs of the trapezoid.
Question 7.
four congruent sides ______________
Answer: square and rhombus.
Explanation:
square:
– It has four sides and four vertices
– Each vertex has an angle equal to 90 degrees
– The sides are equal and parallel.
Rhombus: It 4 congruent sides. The opposite sides are parallel.
Question 8.
Mathematical PRACTICE Model Math Write a real-world problem that involves classifying a quadrilateral Then solve the problem.
Answer:
– Table: It is made of a rectangular top and is supported by four legs.
– A TV set is a rectangular quadrilateral.
– Washing machines, refrigerators, and other home appliances come in rectangular and square shapes.
Vocabulary Check
Fill in each blank with the correct term or number to complete each sentence.
Question 9.
A rectangle is a parallelogram with ____________ right angles.
Answer:
A rectangle is a parallelogram with four right angles.
A rectangle is a four-sided polygon in which the opposite sides are parallel and equal to each other. It is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. The rectangle is a special type of parallelogram with all its angles equal.
Question 10.
A trapezoid is a quadrilateral with exactly ____________ pair of parallel sides.
Answer:
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
A trapezium is a quadrilateral with exactly one pair of parallel sides. One pair of opposite sides is parallel and the other pair is not parallel.
Test Practice
Question 11.
Which statement about the figures shown below is true?
(A) Figures K and N are rectangles.
(B) Figures L and N are quadrilaterals.
(C) Figures K and N are parallelograms.
(D) Figures M and N are parallelograms.
Answer: Option C is the correct answer.
Expalantion:
Both rectangles and parallelograms are quadrilaterals, which means that they are polygons with four sides.
since it has two sets of parallel sides and two pairs of opposite sides that are congruent, a rectangle has all the properties of a parallelogram. That’s why a rectangle is always a parallelogram. However, a parallelogram is not a rectangle.
The explanation for remaining options that are not correct:
– Figure L is not a quadrilateral.
– a parallelogram is not a rectangle.
– Figure M is having only one pair of parallel sides.