We included HMH Into Math Grade 3 Answer Key PDF Module 19 Review to make students experts in learning maths.

Vocabulary

Choose the correct term from the Vocabulary box to complete the sentence.

Vocabulary
closed shape
line segment
open shape
right angle
vertex

Question 1.
A ___________ is an angle that forms a square corner.
More about right angle: A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure. We can see many real-life examples of the right angles in our daily life. For example, the corner of a book, edges of the cardboard, etc. Any shape that is a square or a rectangle, will have its corners equal to 90 degrees or right angle. A right angle is hence called a 90-degree angle.

Question 2.
Each side in a polygon is a ___________.
A 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 triangle with three sides. A circle is also a plane figure but it is not considered a polygon, because it is a curved shape and does not have sides or angles. Therefore, we can say, all the polygons are 2d shapes but not all the two-dimensional figures are polygons.
Polygon shapes:

Concepts and Skills

Question 3.
Use Tools Select all the shapes that appear to have a right angle. Tell what strategy or tool you will use to solve the problem, explain your choice, and then find the answers.

More about right angle: A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure. We can see many real-life examples of the right angles in our daily life. For example, the corner of a book, edges of the cardboard, etc. Any shape that is a square or a rectangle, will have its corners equal to 90 degrees or right angle. A right angle is hence called a 90-degree angle.

Right angle triangle: A right-angled triangle is one that has three sides, “base” “hypotenuse” and “perpendicular” with the angle between the base and the perpendicular is 90°. In the right triangle, the hypotenuse is the longest side and is opposite the right angle of the triangle.
– Every quadrilateral has 4 vertices, 4 angles, and 4 sides
– The total of its interior angles = 360 degrees

Question 4.
Write polygon or not a polygon to describe the shape.

Polygon: A polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides). A minimum of three line segments is required to connect end to end, to make a closed figure. Thus a polygon with a minimum of three sides is known as Triangle and it is also called 3-gon. An n-sided polygon is called n-gon.

1st diagram is a polygon, By definition, we know that the polygon is made up of line segments.
2nd diagram is not a polygon because there is a curve. According to the definition, polygon should not be in curve shapes.
3rd diagram is an open shape polygon. A polygon is open when the segments do not all connect at the beginning and end. That is, if we draw the polygon starting at one point, we finish drawing at a different point

Question 5.
Write the number of sides and the number of angles for this shape.

a pentagon is a two-dimensional figure having 5 sides and 5 angles. In a pentagon, an angle is formed when the two sides of the pentagon share a common point. Since the number of vertices in a pentagon is five, the number of angles in a pentagon is five.
– 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.
– the sum of interior angles of a pentagon is 540°.
– the sum of exterior angles of a pentagon=360°.
– The five sides do not intersect.

Question 6.
Draw a polygon that has exactly 3 sides and exactly 3 angles.
A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides. In other words, a triangle is defined as a three-sided two-dimensional figure whose interior angles are equal to 180°.

Properties of a triangle:
– 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.

Question 7.
A square and a rhombus are shown.

Select all the attributes that these shapes always have in common.
(A) number of sides
(B) number of angles
(C) right angle
(D) angles greater than a right angle
(E) angles less than a right angle
(F) all sides are of equal length

A square and a rhombus both have sides equal in length. But square has all its angles equal to 90 degrees, but a rhombus only has its opposite angles equal.
More common attributes:
– A square is a quadrilateral. A rhombus is also a quadrilateral.
– Opposite sides are parallel to each other. The opposite sides of a rhombus are also parallel to each other.
– Diagonals are perpendicular to each other. Similar to that of a square, the diagonals are of a rhombus are also perpendicular to each other.
– The sum of interior angles of a square is 360 degrees. The sum of interior angles of a rhombus is 360 degrees.
– If “a” is the side length of a square, then its perimeter is 4a units. If “a” is the side length of a rhombus, then its perimeter is 4a units.

Question 8.
When a trapezoid is defined as a quadrilateral that has exactly 1 pair of sides the same distance apart, what shape is always a quadrilateral and never a parallelogram?
(A) rhombus
(B) rectangle
(C) square
(D) trapezoid

Any quadrilateral which does not have its opposite sides being parallel is not a parallelogram. An ordinary quadrilateral with no equal sides is not a parallelogram.
– A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.
– According to the definition, It does not consider a parallelogram to be a trapezoid.

Question 9.
When a trapezoid is defined as a quadrilateral that has at least 1 pair of sides the same distance apart, select all the words that can describe a square.
(A) parallelogram
(B) trapezoid
(C) rectangle