Geometry | Math | Chapter 1 | Grade 5 | With Exercises Solution

GEOMETRY - Math Chapter-1, Grade 5:

Objectives:

Students will be able to:
Identify points, line, line segment and curved lines.
Name and measure angles upto 180°.
Draw the angles, triangles and measure their sides and angles.
Measurement of unknown angle of triangles and quadrilateral.

Outcomes:

Students will have learnt the properties of triangles and quadrilaterals.

Materials:

Collection of different size and shape of triangles and quadrilaterals made of chart papers, wooden blocks, straws, stick, pencil, protractor, rulers, etc.

1.1 Measurement of angles/button

We use protractor to measure angles. Angle contains two arms and a vertex.

Here,
O is a vertex.
AO and OB are two arms.
∠AOB = 60°

How to construct an angle with protractor?
We can use a protractor for the construction of a certain measure of an angle. We can also construct certain angle using a compass too.

Also Check:

Steps to construct and angle with the help of protractor.
Let's construct ∠AOB = 75°.

Remember, you need to exactly overlay the base of the protractor with the base arm of the angle (OA). The centre point of the protractor should be just over the vertex (O) of the angle. alert-info

Step 1: Draw an arm OA with O as it's centre.

Step 2: Overlay the base of your protractor on the base arm OA with center at O.

Step 3: Count round the edge from 0° to 75° and mark B.

Step 4: Remove the protractor and join OB. The angle thus formed is 75°. ∴ ∠AOB = 75°.

1.2 Types of angles/button

Angles are categorized into different types according to their values over the certain range. The angles are categorized into 6 different types of angles on the basis of their sizes. They are -

a. An Acute Angle
b. A Right Angle
c. An Obtuse Angle
d. Straight Angle
e. Reflex Angle
f. Complete turn

a. An Acute Angle: #What is an Acute Angle? #Define Acute angle.

∴ An angle between 0° and 90° is called acute angle.

b. A Right Angle: #What is a Right Angle? #Define Right angle.

∴ An angle whose measurement is exactly 90° is called a right angle.

c. An Obtuse Angle: #What is an Obtuse Angle? #Define Obtuse Angle.

∴ An angle more than 90° and less than 180° is called an obtuse angle.

d. Straight Angle: #What is a Straight Angle? #Define Straight Angle.

∴ An angle whose measurement is exactly 180° is called straight angle.

e. Reflex Angle: #What is Reflex Angle? #Define Reflex Angle.

∴ An angle more than 180° and less than 360° is called a reflex angle.

f. Complete Turn: #What is Complete Turn? #Define Complete Turn.

∴ An angle whose measurement is exactly 360° is called a complete turn.

A glance over the type of angles and their range of values:/button

S.N.	Types of angle	Size	Examples
1	Acute angle	between 0° and 90°	30°, 45°, 60°, 80°, 85°, etc.
2	Right angle	exactly 90°	90°
3	Obtuse angle	between 90° and 180°	95°, 100°, 120°, 150°, 170°, 175°, etc.
4	Straight angle	exactly 180°	180°
5	Reflex angle	between 180° and 360°	185°, 190°, 210°, 245°, 275°, 290°, 315°, 330°, 355°, etc.
6	Angle of a complete turn	exactly 360°	360°

Grade 5: Math Subject-Chapter:1 - GEOMETRY: Exercise 1.1 (With Solution)/button

1. Write the size of each angle. State whether they are acute, right, obtuse or straight line.

For example, ∠ABC = 60°. It is an acute angle.
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2. Draw the following angles with the help of a protractor.

a. 30°
b. 45°
c. 60°
d. 75°
e. 90°
f. 105°
g. 120°
h. 160°
i. 270°
j. 350°
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3. Answer the following questions.

a. How do you call an angle which is smaller than a right angle?
Answer: Acute angle.

b. How many degrees are there in i) right angle, ii) A straight angle iii) An angle of a complete turn.
Answer:
i) right angle = 90°.
ii) A straight line = 180°.
iii) An angle of a complete turn = 360°.

c. Show that 180° is two right angles.
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d. Show that 360° is a four right angles.
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e. What do you call an angle which is greater than a right angle and less than a straight angle?
Answer: Obtuse angle.

f. Is 270° a reflex angle or obtuse angle? Why? Give reasons.
Answer: 270° is a reflex angle because it is less than 360° and is more than 180°. The reason is that an angle which is more than 180° and less than 360° is called a reflex angle.

4. Categorize the following angles as acute, right, obtuse, straight, reflex and the angle of complete turn.
10°, 38°, 92°, 180°, 45°, 270°, 23°, 180°, 90°, 60°, 30°, 36°, 350°, 360°.
Answer:
10° = Acute angle.
38° = Acute angle.
92° = Obtuse angle.
180° = Straight angle.
45° = Acute angle.
270° = Reflex angle.
23° = Acute angle.
180° = Straight angle.
90° = Right angle.
60° = Acute angle.
30° = Acute angle.
36° = Acute angle.
350° = Reflex angle.
360° = Angle of a complete turn.

5. Guess the measurement of following angle without measuring them. Then compare this result after measuring them by protractors. See, how accurate you are.
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6. Copy the similar figures in your exercise book and measure each angle of these following triangles.
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1.3 Perpendicular line/button

In above figure, a straight line segment CD meets another line segment AB at point D and makes an angle of 90. Here CD is called a perpendicular to AB. So, when a straight line (CD) meets another straight line thereby making an angle of 90, they are called perpendicular to each other.

#How to draw a perpendicular line?
Steps to draw perpendicular line are as follows:

Step 1: Draw a straight line AB.

Step 2: Mark point D where perpendicular line is to be drawn.

Step 3: Overlay the centre of the protractor at point D and mark the point outside the protractor at 90. Name the marked point as C.

Step 4: Join C and D. CD is now perpendicular to AB.

1.4 Intersecting line segment/button

In above figures, a straight line segment AB crosses another line segment CD at point O. Here, straight line segments AB and CD are called intersecting lines. The point O is called the point of intersection.