We included HMH Into Math Grade 3 Answer Key PDF Module 19 Lesson 1 Describe Shapes to make students experts in learning maths.
HMH Into Math Grade 3 Module 19 Lesson 1 Answer Key Describe Shapes
I Can describe shapes as open or dosed, as polygons, and by the number of sides and the number of angles.
Spark Your Learning
Rory uses a 3D printer to make a model of a steel gate for a sculpture garden. She draws this design by using a computer program. When reviewing her work, she sees different shapes within her gate design. What are some shapes that Rory may see?
Draw and describe some shapes that Rory may see within the gate.
Answer: The Rory may see the shapes are triangle, square, right-angled triangle, hexagon, trapezium.
Now one by one will describe the shapes Rory see:
Square: Square is a regular quadrilateral, which has all four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees. A square can also be defined as a rectangle where two opposite sides have equal length.
Properties:
– All four interior angles are equal to 90°
– All four sides of the square are congruent or equal to each other
– The opposite sides of the square are parallel to each other
– The diagonals of the square bisect each other at 90°
– The two diagonals of the square are equal to each other
– The square has 4 vertices and 4 sides
– The diagonal of the square divide it into two similar isosceles triangles.
– The length of diagonals is greater than the sides of the square
Now describing triangle shape:
– A triangle is a polygon with three sides having three vertices.
– The sum of the interior angles of a triangle is 180 degrees
– When two sides of a triangle are added, it is always greater than the third side
– Similarly, if the two sides of a triangle are subtracted, it is
always less than the third side
– Two triangles are said to be similar if the corresponding angles are congruent and the corresponding side lengths are proportional.
Right-angled triangle:
A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle. The third side is called the hypotenuse, which is the longest side of all three sides. The side opposite to the right angle is the smallest side.
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.
Trapezium:
A trapezium is a closed shape or a polygon, that has four sides, four corners/vertices and four angles. Any pair of opposite sides of a trapezium are parallel to each other.
– In trapezium, exactly one pair of opposite sides are parallel
– The diagonals intersect each other.
Turn and Talk Compare the shapes you found with a classmate. How are your descriptions alike? How are they different?
Answer: the shapes are triangle, square, right-angled triangle, hexagon, trapezium.
By comparing one another they are different in shape and each shape has its own properties.
For example, if we compare by their sides and angles then
– The triangle is a three-sided polygon (2d Shape) that has three edges and three vertices. The sum of all the three angles of a triangle is equal to 180°.
– The square is a four-sided polygon (2d Shape), whose four sides are equal in length and all the angles are equal to 90°. It is considered to be a two-dimensional regular quadrilateral
– The right-angled triangle looks like the shape and angles are A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.
– Hexagon has six sides and the sides are sometimes equal and unequal. And angles are also equal and unequal.
– The trapezium looks like a closed shape or a polygon, that has four sides, four corners/vertices and four angles. Any 1 pair of opposite sides of a trapezium are parallel to each other.
Build Understanding
Question 1.
Shapes A, B, C, and D are all alike in one way.
Connect to Vocabulary
A closed shape is a shape that begins and ends at the same point.
An open shape is a shape that does not begin and end at the same point.
A plane shape is a shape on a flat surface that is formed by curved paths, line segments, or both.
A line segment is straight. It is part of a line and has two endpoints.
A. Circle the closed shapes. Draw a box around
Answer:
Closed shapes: Any enclosed shape that does not have any open ends and can be traced back from where it started without any break is known as a closed shape.
In geometry, you have seen examples of closed shapes in the above section. Now, let us look at some real-life examples of closed shapes. Examples are clouds, stars, signboards.
B. Why are the shapes you circled called closed shapes?
Answer:
Shapes are closed shapes that are created by joining lines together. Closed shapes made of four straight lines are called quadrilateral shapes. And moreover, the shape is enclosed from all sides end-to-end and form a figure with no openings that’s why I circled those shapes.
C. Why are the shapes you drew a box around called open shapes?
Answer:
Any shape in which the start point and the endpoint is different and not connected is called an open shape. Open shapes are not continuous and cannot be traced without any break.
D. How are shapes A, B, C, and D alike?
Answer:
The shape A is a right-angled triangle. This can be described as:
A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle. The third side is called the hypotenuse, which is the longest side of all three sides. The side opposite to the right angle is the smallest side.
The shape B is a circle. This can be described as:
The circle is a two-dimensional figure, which has its area and perimeter. The perimeter of the circle is also called the circumference, which is the distance around the circle.
The shape C is a hexagon. This can be described as:
Hexagon has six sides and the sides are sometimes equal and unequal. And angles are also equal and unequal.
The shape D is a rhombus. This can be described as:
A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles.
Question 2.
Look at these two shapes.
A. How are they different?
Answer:
The difference in both shapes can be explained below:
The shape A is formed with curved lines.
The shape B is formed with straight lines.
B. Draw a closed shape formed by line segments. Draw an open shape that has at least one curved path.
Answer:
First, know what is line segment?
Definition: A line segment has two definite endpoints in a line. The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimetres (cm), millimetres (mm) or by conventional units like feet or inches.
– A closed line segment consists of both endpoints, whereas an open line segment is exclusive of the two endpoints. A line segment that has exactly one endpoint is called a half-open line segment.
Question 3.
These shapes are alike.
A. What attributes do all the shapes share?
These shapes are all polygons.
Answer:
The above-given shapes are closed shapes.
A triangle has 3 straight sides. Triangles can be big or small. Triangles can be any colour. Any closed shape with 3 straight sides is a triangle.
– Rectangle has 4 sides. It can be big or small. Any closed shape with four sides is called a quadrilateral. The rectangle is one of the quadrilaterals.
– The shape which is in red colour has 7 corners and 7 sides are called a heptagon.
– The shape which is in blue colour is the star. It has 5 sides and 5 corners are called the pentagon.
Connect to Vocabulary
A polygon is a closed plane shape with straight sides that are line segments. Each line segment in a polygon is aside.
B. Draw a polygon. Circle the angles and put an X on the sides.
Answer:
The rectangle is a polygon because it has four sides with straight lines and it is a closed figure with a straight line segment.
X is represented on all sides of the rectangle. The angles place were circled.
Connect to Vocabulary
Plane shapes have angles formed by two line segments that share an endpoint called a vertex.
Question 4.
Polygon A has 4 sides and 4 angles. How many sides and angles does Polygon B have?
Answer:
Polygon A is a rectangle that has four sides and four angles.
Polygon B is a pentagon that has five sides and 5 angles.
The angles formed by two adjacent pairs of sides are called interior angles of a pentagon.
Number of sides = Number of vertices = Number of interior angles = 5
Two interior angles that share a common side are called adjacent angles or adjacent interior angles.
Turn and Talk How is a polygon different from another plane shape?
Answer:
Both have an unlimited amount of shapes, all of different sizes, and areas. Some shapes are big, some are small; some have lengths of different sizes making for different areas.
Plane shapes are just flat surfaces extending infinitely in all directions (e.g. horizontal or vertical plane). For example, a square. A square is a shape with 4 lengths of equal size.
A polygon is a plane figure bounded by edges that are all straight lines.
Check Understanding
Question 1.
Circle the open shape. Put an X on the closed shape.
Answer:
closed shape: Closed shapes: Any enclosed shape that does not have any open ends and can be traced back from where it started without any break is known as a closed shape.
In geometry, you have seen examples of closed shapes in the above section. Now, let us look at some real-life examples of closed shapes. Examples are clouds, stars, signboards.
Open shaped figure: Any shape in which the start point and the endpoint is different and not connected is called an open shape. Open shapes are not continuous and cannot be traced without any break.
Question 2.
How many sides and angles does this polygon have?
Answer:
The above-given diagram is a parallelogram.
It has four sides and four angles.
More about parallelogram:
A quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, and then the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length.
On Your Own
Question 3.
Critique Reasoning Dante says that all closed plane shapes are polygons. Is Dante correct? Explain your answer.
Answer: yes, Dante is correct.
A polygon is a closed figure, formed by segments, and its sides do not cross. The following figures are polygons.
Question 4.
Social Studies Mya uses a map to study some of the western states in the United States. Some states have a border in the shape of a polygon. Name one state that could be in the shape of a polygon. Explain how you know.
Answer:
The marked states in the above diagram are polygons.
Polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges. The point where two line segments meet is called vertex or corners, henceforth an angle is formed. An example of a polygon is a square with four sides.
Is the shape a polygon? Write yes or no.
Question 5.
Answer: yes
The above shape is polygon because it has 3 sides and 3 vertices and it is made up of straight-line segments connected to each other end to end. But it is irregular shape.
Question 6.
Answer: No
The above-given shape is an open shape figure that’s why it is not a polygon.
Actually, Polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges. The point where two line segments meet is called vertex or corners, henceforth an angle is formed. An example of a polygon is a square with four sides.
Question 7.
Answer: No
The above-given shape is not a polygon because it is having a curved shape. In polygons, the sides are made of straight line segments connected to each other end to end.
Write the number of sides and the number of angles.
Question 8.
________ sides
________ angles
Answer: 3 sides and 3 angles.
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°.
– 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.
Question 9.
________ sides
________ angles
Answer: 8 sides and 8 angles
An eight-sided shape is a polygon called an octagon. It has eight straight sides that meet at eight corners
The sum of interior angles of a polygon having 8 sides are 1080 degrees.
I’m in a Learning Mindset!
What helps me remember the names of different attributes of shapes?
Answer:
I think making shapes with clay and making shapes with straws and then reading the attributes.
Sorting out the shapes from the given pictures also easily we can remember the attributes.