We included HMH Into Math Grade 3 Answer Key PDF Module 20 Categorize Two-Dimensional Shapes to make students experts in learning maths.
HMH Into Math Grade 3 Module 20 Answer Key Categorize Two-Dimensional Shapes
Can You find the mystery shape?
- Read the list of clues.
- Use the clues to identify the mystery shape.
Clues:
- I am formed with only line segments.
- I have exactly four vertices.
- Exactly three of my sides have the same length.
What is the mystery shape? _________
Answer:
Turn and Talk
Are there any other shapes that match the description in the third clue? Explain.
Answer:
How did you decide that the shape you chose fit all of the clues?
Answer:
Are You Ready?
Complete these problems to review prior concepts and skills you will need for this module.
Draw Two-Dimensional Shapes
Question 1.
Draw a rectangle.
Answer:
A rectangle is a two-dimensional plane figure with four sides. 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. A rectangle with four equal sides is known as a square.
Properties of rectangle:
The fundamental properties of rectangles are:
– A rectangle is a quadrilateral
– The opposite sides are parallel and equal to each other
– Each interior angle is equal to 90 degrees
– The sum of all the interior angles is equal to 360 degrees
– The diagonals bisect each other
– Both the diagonals have the same length
– A rectangle with side lengths a and b has the perimeter as 2a+2b units
– A rectangle with side lengths a and b has the area as ab sin 90 = ab square units
– The sum of the interior angles is equal to 360 degrees
– A diagonal of a rectangle is the diameter of its circumcircle
– The diagonals bisect each other at different angles. One is acute, and another one is an obtuse angle
– If the two diagonals bisect each other at right angles, then the rectangle is known as a square
– A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the longer parallel sides. In this case, the height of the cylinder is equal to the width of a rectangle. Also, the cylinder diameter is equivalent to the length of a rectangle
– A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the shorter parallel sides. In this case, the height of the cylinder is equal to the length of a rectangle. Similarly, the cylinder diameter is equivalent to the width of a rectangle.
Question 2.
Draw a trapezoid.
Answer:
4 sides and 4 vertices
The trapezium is a quadrilateral with one pair of parallel opposite sides. The parallel sides of a trapezium are called bases and the non-parallel sides of a trapezium are called legs. It is also called a trapezoid. Sometimes the parallelogram is also called a trapezoid with two parallel sides.
Properties:
Some important properties of a trapezium are as follows:
– In trapezium, exactly one pair of opposite sides are parallel
– The diagonals intersect each other
– The non-parallel sides in the trapezium are unequal except in isosceles trapezium
– The line that joins the mid-points of the non-parallel sides is always parallel to the bases or parallel sides which is equal to half of the sum of parallel sides
Sides and Vertices
Write the number of sides and vertices that the shape has.
Question 3.
_________ sides
_________ vertices
Answer: 4 sides and 4 vertices
The trapezium is a quadrilateral with one pair of parallel opposite sides. The parallel sides of a trapezium are called bases and the non-parallel sides of a trapezium are called legs. It is also called a trapezoid. Sometimes the parallelogram is also called a trapezoid with two parallel sides.
Properties:
Some important properties of a trapezium are as follows:
– In trapezium, exactly one pair of opposite sides are parallel
– The diagonals intersect each other
– The non-parallel sides in the trapezium are unequal except in isosceles trapezium
– The line that joins the mid-points of the non-parallel sides is always parallel to the bases or parallel sides which is equal to half of the sum of parallel sides
Question 4.
_________ sides
_________ vertices
Answer: 3 sides; 3 vertices
By the definition of triangle, we know that it is a closed polygon that consists of three sides and three vertices. Also, the sum of all three internal angles of a triangle is equal to 180°.
Properties of the triangle:
The properties of the triangle are:
– The sum of all the angles of a triangle (of all types) is equal to 180°.
– The sum of the length of the two sides of a triangle is greater than the length of the third side.
– In the same way, the difference between the two sides of a triangle is less than the length of the third side.
– The side opposite the greater angle is the longest side of all the three sides of a triangle.
– The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property.
– Two triangles are said to be similar if the corresponding angles of both triangles are congruent and the lengths of their sides are proportional.
– Area of a triangle = ½ × Base × Height
– The perimeter of a triangle = sum of all its three sides
Question 5.
_________ sides
_________ vertices
Answer: 6 sides and 6 vertices.
A closed figure which is two-dimensional and is made up of straight lines is called a polygon. A polygon is a geometric figure. In this type of geometric figure, if one has 6 sides, it is called a Hexagon.
Properties of hexagon:
1. Sides: A Hexagon has six sides.
2. Angles: A Hexagon has six angles.
3. Diagonals: There is a total of 9 diagonals in a hexagon.
4. Interior angles: The sum of interior angles of a hexagon is 720 degrees.
5. A measure of the angle: Each interior angle of a hexagon is 120 degrees.
6. Exterior angles: The sum of all the exterior angles is equal to 360 degrees.
7. The measure of the angles: Each exterior angle of a hexagon is of 60 degrees.
8. Area: The area of the hexagon is (1.5 √3) × s2
9. Triangles: The hexagon is made up of 6 regular triangles.
Question 6.
Circle the shapes that have more than 4 sides and 4 vertices.
Answer:
Explanation:
Pentagon and hexagon are the two shapes that have more than 4 sides and 4 vertices.
Pentagon: A pentagon is a five-sided polygon (2d Shape), and it can be regular or irregular. In the case of a regular pentagon, each interior angle is equal to 108°, and each exterior angle measures 72°. It has five diagonals. The Pentagon building, which is the headquarters of the US Department of Defense, is a great example of the pentagon shape.
A regular hexagon is a closed shape polygon that has six equal sides and six equal angles. In the case of any regular polygon, all its sides and angles are equal.
Properties of hexagon:
– It has 6 equal sides and 6 equal angles.
– It has 6 vertices.
– The Sum of interior angles equals 720°.
– The Interior angle is 120° and the exterior angle is 60°.
– It is made up of six equilateral triangles.
– 9 diagonals can be drawn inside a regular hexagon.
– All the sides opposite to each other are parallel.