We included HMH Into Math Grade 3 Answer Key PDF Module 19 Lesson 2 Describe Angles in Shapes to make students experts in learning maths.
HMH Into Math Grade 3 Module 19 Lesson 2 Answer Key Describe Angles in Shapes
I Can identify angles that are right angles, greater than a right angle, or less than a right angle in shapes.
Spark Your Learning
Felix wrote this riddle:
I am a closed shape with at least 3 angles and 3 sides. My sides are not all equal in length, but all my angles are equal. What shape am I?
Draw and name a shape to solve the riddle.
Answer: Triangle
Explanation:
Similar triangles have the same basic shapes. Triangles having the same angles but different sizes are called Similar Triangles as the ratio of the sides remains the same. The rotated triangles or the mirror image triangles are also called Similar triangles as the angles and sizes are the same.
– The ratio of the corresponding sides of two similar triangles is the same.
– The corresponding angles of two similar triangles are congruent.
Turn and Talk Help Felix write another riddle that describes a shape. What shape does the riddle describe? Why does this shape solve the riddle?
Answer: A scalene triangle
Explanation of scalene triangle:
A triangle in which all the sides are of different lengths is called Scalene Triangle.
Properties:
– A scalene triangle has all the sides different.
– It has unequal angles.
– Its longest side is right opposite to its biggest angle.
– It cannot be bisected into two equal halves.
– It has no line of symmetry.
– A scalene triangle can be an acute scalene triangle, an obtuse scalene triangle or a right scalene triangle.
Build Understanding
Question 1.
Sanjay makes a coloring book with different shapes to color. One of the shapes is shown below. How can you describe the angles of this shape?
A. Use a square corner from a sheet of paper like this one to check the angles in Sanjay’s shape.
Connect to Vocabulary
A right angle is an angle that forms a square corner.
The blue square marks a right angle.
Answer: An angle is formed when two rays are joined together at a common point.
The angle which is exactly 90 degrees is called the right angle.
B. Circle the right angles, or square corners, in Sanjay’s shape.
Answer:
What is the right angle?
If the measure of the angle between two rays is exactly equal to 90 degrees or π/2, then the angle is called a right angle.
C. Draw an X on the vertex of the angles that are not right angles. How do you know these are not right angles?
Answer: I had shown in the below diagram:
How do we know?
There are some standard forms are there to represent the angles.
There are acute angle, obtuse angle, right angle, straight angle, and reflect angle.
Angles that measure less than 90° such as 87°, 56°, 77°, 42°, etc., are acute angles.
Angles that measure more than 90° such as 91°, 98°, 102°, 150°, 167°, etc., are called obtuse angles.
The angle that measures exactly 90° is called the right angle.
The angle that measures half of the area means 180° which is called a straight angle.
The angle that measures total area means 360° which is called reflect angle.
D. The closed shape has _________ sides and ________ angles. It has 1 _________ and ________ angles that are not right angles.
Answer:
The closed shape has 4 sides and 4 angles. if it has 1 side and 1 angle then those are not right angles.
Turn and Talk Are all right angles the same? Explain.
Answer: That all right angles are equal to one another.
It just says that whenever we create a right angle by establishing perpendiculars, the angles so created are always the same.
* when a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle. And the straight line which stands on the other is called perpendicular to it.
Question 2.
The blue angles are right angles.
• The red angle is greater than a right angle.
• The yellow angle is less than a right angle.
Use a square corner to compare the angles in the shapes to a right angle.
A. Draw a small square to show each right angle.
Answer:
According to the above diagram, we can write the right angle:
I named diagrams A and B
The shape A is called parallelogram, B is like a pentagon because it has 5 sides and 5 corners.
The question asked was to draw a small square.
In shape A, I cannot draw a square; if we draw a diagonal also I cannot draw a square. Because the angle in the square is 90 degrees. But in a parallelogram, the angles are not right angles. The angles in the parallelogram are obtuse angles. I cannot make a right angle in the parallelogram.
Angles of parallelogram: A parallelogram is a flat 2d shape that has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, which means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.
In shape B, I can draw a square because there are square corners that can easily draw 90 degrees angles.
B. Draw a circle around the vertex of each angle that is greater than a right angle. Shade the vertex of each angle that is less than a right angle.
Answer:
There are some standard forms are there to represent the angles.
There are acute angle, obtuse angle, right angle, straight angle, and reflect angle.
Angles that measure less than 90° such as 87°, 56°, 77°, 42°, etc., are acute angles.
Angles that measure more than 90° such as 91°, 98°, 102°, 150°, 167°, etc., are called obtuse angles.
The angle that measures exactly 90° is called the right angle.
The angle that measures half of the area means 180° which is called a straight angle.
The angle that measures total area means 360° which is called reflect angle.
The opposite angles of a parallelogram are parallel to each other. A Parallelogram has parallel sides. It means that two angles will be acute and two angles will be obtuse. Since the parallelogram leans over, the angle measure of the obtuse angle will be greater, and the measure of acute angle will be smaller
according to that, I circled greater than 90 and less than 90 degrees.
C. Draw a shape that has exactly 3 right angles in the workspace above.
Answer:
you can make a four-sided shape with right-angles, but it must have another right angle too. So I think its square.
Check Understanding
Write right angle, greater than a right angle, or less than a right angle for the blue angle.
Question 1.
Answer: less than right angle.
Less than a right angle is an acute angle.
Acute angle: An angle which is measuring less than 90 degrees is called an acute angle.
Properties:
– All equilateral triangles are acute triangles. An equilateral triangle has three sides of the same length and three angles of the equal measure, i.e. 60°
– Opposite the highest angle is the longest side of an acute triangle
– Acute triangles can be isosceles, equilateral, or scalene
Question 2.
Answer: equal to 90 degrees.
The right angle is exactly 90 degrees.
If the measure of the angle between two rays is exactly equal to 90 degrees or π/2, then the angle is called a right angle.
We know that all the interior angles of a square are right angles, i.e. equal to 90 degrees
Question 3.
Answer: greater than 90 degrees.
In Mathematics, an obtuse angle is an angle that is greater than 90 degrees and less than 180 degrees.
Every hexagon has six sides and six angles and every hexagon is made up of six angles of 120-degrees.
On Your Own
Question 4.
Reason Tim cuts a rectangular tile on the diagonal from the top left to the bottom right corners.
Before the cut, there are __________ right angles.
Answer: 4 right angles
Before they cut it was a rectangle. A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all four vertices are equal to 90 degrees
Properties:
– It has four sides and four vertices
– Each vertex has an angle equal to 90 degrees
– The opposite sides are equal and parallel
– Diagonals bisect each other
– Perimeter is equal to twice of 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
After the cut, there are _______ right angles and ________ angles that are _________ than right angles.
Answer: 2 right angles and the other two angles are less than 90 degrees.
It is the right triangle.
What is the right triangle?
A triangle in which one of the measures of the angles exactly 90 degrees is called a right triangle. In the triangle given below, one of the three angles of the triangle is 90 degrees whereas the other two angles are less than 90 degrees.
Properties:
– Out of the three angles of a right-angled triangle, one angle is greater than 90 degrees and the other two are acute angles.
– The longest side of the right triangle is called the hypotenuse and the angle opposite to the hypotenuse is 90 degrees.
– The area of a right triangle is half the product of the base and height.
– The radius of the circumcircle is always half the hypotenuse and the centre of the circumcircle is always the midpoint of the hypotenuse.
– A-line perpendicular to the hypotenuse from the right angle results in three similar triangles.
Write the total number of each kind of angle. Draw a small square to mark what appears to be a right angle.
Question 5.
________ right
_________ less than right
_________ greater than right
Answer:
one right angle
two angles less than right angle
one angle greater than right angle.
Question 6.
________ right
_________ less than right
_________ greater than right
Answer:
one right angle
two angles less than right angle
one angle greater than right angle.
Question 7.
STEM The incoming and outgoing angles of a reflected light beam are always equal. Angle A is formed by the reflected light beam. Is Angle A a right angle, greater than a right angle, or less than a right angle?
Answer: less than right angle
for this we need to learn some basics angle of incidence and angle of reflection.
If we draw a perpendicular line in the middle then we will know the angle of reflection.
The angle of incidence be X
then the angle of reflection will be 90-X, so according to this definitely it will be less than the right angle.
I’m in a Learning Minds!
How effective is using a corner of a sheet of paper to identify right angles and other angles? Explain.
Answer: