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

## HMH Into Math Grade 3 Module 19 Review Answer Key

**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.

Answer: Right angle.

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 ___________.

Answer: a line segment

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.

Answer:

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.

Quadrilateral: A quadrilateral is a 4-sided plane figure. Below are some important properties of quadrilaterals :

– 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.

Answer:

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.

Answer:

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.

Answer:

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

Answer: F

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

Answer: Option D is correct.

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

(D) quadrilateral

(E) triangle

(F) rhombus

Answer:

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.