883
edits
Changes
From Karnataka Open Educational Resources
no edit summary
=Learning Objectives=
=Learning Objectives=
* Identify a triangle
* Identify a triangle
* Recognize interior and exterior angles
* Recognize interior and exterior angles
* Classifying types of triangles
* Classifying types of triangles
* Recognize the angle sum property
* Recognize the angle sum property
* Establish relation between interior and exterior angles
* Establish relation between interior and exterior angles
==Teaching Outlines==
==Teaching Outlines==
== Concept #1. Formation of a triangle, elements of a triangle and its measures ==
== Concept #1. Formation of a triangle, elements of a triangle and its measures ==
# A triangle is a three sided closed figure.
# A triangle is a three sided closed figure.
# It is one of the basic shapes in geometry.
# It is one of the basic shapes in geometry.
# It triangle is a polygon with three edges and three vertices.
# It triangle is a polygon with three edges and three vertices.
# There are three angles in a triangle formed at the three vertices of the triangle.
# There are three angles in a triangle formed at the three vertices of the triangle.
# Interior and exterior angles in a triangle at a vertex, together form a linear pair.
# Interior and exterior angles in a triangle at a vertex, together form a linear pair.
=== '''Activity No # 1 : Formation of a triangle''' ===
=== '''Activity No # 1 : Formation of a triangle''' ===
[[File:Triangle formation.png|thumb|Formation of a triangle]]
[[File:Triangle formation.png|thumb|Formation of a triangle]]
* '''Objectives'''
* '''Objectives'''
# Understand formation of triangles
# Understand formation of triangles
# Recognize elements of triangle
# Recognize elements of triangle
# Introduce concepts of exterior angle.
# Introduce concepts of exterior angle.
* '''Pre-requisites'''
* '''Pre-requisites'''
Prior knowledge of point, lines, angles, parallel linesResources needed
Prior knowledge of point, lines, angles, parallel linesResources needed
# Digital : Computer, geogebra application, projector.
# Digital : Computer, geogebra application, projector.
# Non digital : Worksheet and pencil
# Non digital : Worksheet and pencil
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/z4h42k8z Introduction to a triangle.ggb]”'''
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/z4h42k8z Introduction to a triangle.ggb]”'''
* '''How to do'''
* '''How to do'''
# Use the geogebra file to illustrate.
# Use the geogebra file to illustrate.
# Digital : Computer, geogebra application, projector.
# Digital : Computer, geogebra application, projector.
# Non digital : Worksheet and pencil,6-8 strings (preferably in different colours)
# Non digital : Worksheet and pencil,6-8 strings (preferably in different colours)
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/hyecxd9u Elements of a triangle.ggb]”'''
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/hyecxd9u Elements of a triangle.ggb]”'''
* '''How to do'''
* '''How to do'''
# Students work individually but in their groups.
# Students work individually but in their groups.
| || ||
| || ||
|-
|-
| || ||
| || ||
|}
|}
12.For each of the triangles observe (inspect visually) which is the longest side and which is the shortest side
{| class="wikitable"
{| class="wikitable"
|-
|-
|
|
|}
|}
13. Allow the students to explore if there is any connection between the two?
14. After the students see the Geogebra file, they can attempt an alternative worksheet like below:
{| class="wikitable"
{| class="wikitable"
|-
|-
| || || || || || || ||
| || || || || || || ||
|}
|}
* '''Evaluation at the end of the activity'''
'''Evaluation at the end of the activity'''
1. Have the students been able to identify the elements in a triangle?
1. Have the students been able to identify the elements in a triangle?
[[Category:Triangles]]
[[Category:Triangles]]
[[Category:Class 9]]
[[Category:Class 9]]
=== '''Activity No # 3 : Measures associated in a triangle''' ===
=== '''Activity No # 3 : Measures associated in a triangle''' ===
# Digital : Computer, geogebra application, projector.
# Digital : Computer, geogebra application, projector.
# Non digital : Worksheet and pencil.
# Non digital : Worksheet and pencil.
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/jjmbu9ed Measures in a triangle.ggb]”'''
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/jjmbu9ed Measures in a triangle.ggb]”'''
* '''How to do'''
* '''How to do'''
# Show the Geogebra file and ask students to record the values of angles and sides that are seen and ask if there is any connection between the side and the angle
# Show the Geogebra file and ask students to record the values of angles and sides that are seen and ask if there is any connection between the side and the angle
# What is the sum of the angles in a triangle?
# What is the sum of the angles in a triangle?
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/q6fnttmn Angles of a triangle.ggb]”'''
# Geogebra files : '''“[https://www.geogebra.org/m/bwsvgqqg#material/q6fnttmn Angles of a triangle.ggb]”'''
* '''How to do'''
* '''How to do'''
# Ask students how many lines are there? They should be able to identify the points of intersection of the lines. How many points of intersection are formed?
# Ask students how many lines are there? They should be able to identify the points of intersection of the lines. How many points of intersection are formed?
# How many angles are formed at an intersecting point? How many angles in total at the three points of intersection?What is the total angle measure at each intersecting point?
# How many angles are formed at an intersecting point? How many angles in total at the three points of intersection?What is the total angle measure at each intersecting point?
# How many angles are inside the triangle and how many are outside the triangle?
# How many angles are inside the triangle and how many are outside the triangle?
# Can you find an exterior angle that is equal to the interior angle of a triangle at each vertex?Why are they equal?
# Can you find an exterior angle that is equal to the interior angle of a triangle at each vertex?Why are they equal?
# Identify the exterior angles that are equal? Justify why they are equal.
# Identify the exterior angles that are equal? Justify why they are equal.
# Establish that there are 2 angles which are exterior of the triangle that are equal and are formed when the sides of the triangle is extended at the vertex.
# Establish that there are 2 angles which are exterior of the triangle that are equal and are formed when the sides of the triangle is extended at the vertex.
# Students to analyze the interior and exterior angle at each point to find a relation between the interior angle and one of the exterior angles at the vertex. Students should be able to recognize the linear pair formed by interior angle and exterior angle.
# Students to analyze the interior and exterior angle at each point to find a relation between the interior angle and one of the exterior angles at the vertex. Students should be able to recognize the linear pair formed by interior angle and exterior angle.
# Vary the position of the lines to check if interior and exterior angles form a linear pair.
# Vary the position of the lines to check if interior and exterior angles form a linear pair.
Note the measure of angles
Note the measure of angles
* '''Evaluation at the end of the activity'''
* '''Evaluation at the end of the activity'''
# Are students able to recognize interior and exterior angles in a triangle
# Are students able to recognize interior and exterior angles in a triangle
# Have the students able to find a relation between the interior angle and exterior angle that are formed at each vertex?
# Have the students able to find a relation between the interior angle and exterior angle that are formed at each vertex?
== Concept 2: Types of Triangles based on sides and angles ==
== Concept 2: Types of Triangles based on sides and angles ==
'''Types of triangles based on angles in the triangle'''
'''Types of triangles based on angles in the triangle'''
# Acute triangles are triangles in which the measures of all three angles are less than 90<sup>o</sup>.
# Acute triangles are triangles in which the measures of all three angles are less than 90<sup>o</sup>.
# Obtuse triangles are triangles in which the measure of one angle is greater than 90<sup>o</sup>.
# Obtuse triangles are triangles in which the measure of one angle is greater than 90<sup>o</sup>.
# Right triangles are triangles in which the measure of one angle equals 90 degrees.
# Right triangles are triangles in which the measure of one angle equals 90 degrees.
'''Types of triangles based on sides in the triangle'''
'''Types of triangles based on sides in the triangle'''
# Equilateral triangles are triangles in which all three sides are the same length.
# Equilateral triangles are triangles in which all three sides are the same length.
# Isosceles triangles are triangles in which two of the sides are the same length.
# Isosceles triangles are triangles in which two of the sides are the same length.
# Scalene triangles are triangles in which none of the sides are the same length.
# Scalene triangles are triangles in which none of the sides are the same length.
=== '''Activity No # 5 : Types of triangles based on sides''' ===
=== '''Activity No # 5 : Types of triangles based on sides''' ===
* '''Objectives'''
* '''Objectives'''
# Recognize the triangles based on the measures of the sides
# Recognize the triangles based on the measures of the sides
* '''Pre-requisites'''
* '''Pre-requisites'''
# Prior knowledge of point, lines, angles, elements of triangle
# Prior knowledge of point, lines, angles, elements of triangle
* '''Resources needed'''
* '''Resources needed'''
# Digital : Computer, geogebra application, projector.
# Digital : Computer, geogebra application, projector.
# Non digital : Worksheet and pencil.
# Non digital : Worksheet and pencil.
# Geogebra files : “5. Types of triangle by sides.ggb”
# Geogebra files : “5. Types of triangle by sides.ggb”
* '''How to do'''
* '''How to do'''
# Students should recognize the elements of a triangle – sides and angles.
# Students should recognize the elements of a triangle – sides and angles.
# What are the measures of the sides of a triangle, are the measurements of the sides equal or different.
# What are the measures of the sides of a triangle, are the measurements of the sides equal or different.
# Establish that different triangles are formed with the different measures of the sides: when all sides are different, when any two sides are equal and when all sides are equal.
# Establish that different triangles are formed with the different measures of the sides: when all sides are different, when any two sides are equal and when all sides are equal.
# Children can note the measures of the sides in the worksheet for different triangles to conclude the type of triangles based on the sides.
# Children can note the measures of the sides in the worksheet for different triangles to conclude the type of triangles based on the sides.
# Is the triangle formed for any measure of the sides. When does the triangle not form. What is the relation between the 3 sides for the triangle to be formed.
# Is the triangle formed for any measure of the sides. When does the triangle not form. What is the relation between the 3 sides for the triangle to be formed.
<nowiki>-----------------</nowiki>
<nowiki>-----------------</nowiki>
* '''Evaluation at the end of the activity'''
* '''Evaluation at the end of the activity'''
# Are children able to recognize the types of triangles when the sides are specified.
# Are children able to recognize the types of triangles when the sides are specified.
# Have children been able to conclude when a triangle is formed given the three sides.
# Have children been able to conclude when a triangle is formed given the three sides.
=== Activity No # 6 : Types of triangles based on angles ===
=== Activity No # 6 : Types of triangles based on angles ===
# Digital : Computer, geogebra application, projector.
# Digital : Computer, geogebra application, projector.
# Non digital : Worksheet and pencil.
# Non digital : Worksheet and pencil.
# Geogebra files : “6. Types of triangle by angle.ggb”
# Geogebra files : “6. Types of triangle by angle.ggb”
* '''How to do'''
* '''How to do'''
# Identify the angle types in the triangle.
# Identify the angle types in the triangle.
# Can the angles in the triangle be of different type – obtuse or right angle.
# Can the angles in the triangle be of different type – obtuse or right angle.
# Establish the types of triangles based on the types of angles that form the triangle – when all angles are acute angles, when one of the angle is a right angle and when one of the angle is obtuse angle.
# Establish the types of triangles based on the types of angles that form the triangle – when all angles are acute angles, when one of the angle is a right angle and when one of the angle is obtuse angle.
# Is it possible to have a triangle with two right angle or two obtuse angle. Why or why not?
# Is it possible to have a triangle with two right angle or two obtuse angle. Why or why not?
# What kind of a triangle is formed when all the angles are equal? For what measure of the angle such a triangle is formed?
# What kind of a triangle is formed when all the angles are equal? For what measure of the angle such a triangle is formed?
# Can a triangle be formed with a reflex angle.
# Can a triangle be formed with a reflex angle.
# Measure the angles for different triangle, recognize the types of angles and conclude the type of triangle.
# Measure the angles for different triangle, recognize the types of angles and conclude the type of triangle.
* '''Evaluation at the end of the activity'''
* '''Evaluation at the end of the activity'''
# Are children able to recognize the types of triangles based on the angles in a triangle.
# Are children able to recognize the types of triangles based on the angles in a triangle.
== Concept 3: Angle Sum Property ==
== Concept 3: Angle Sum Property ==
3. Geogebra files : '''“7a. Angles in a right triangle.ggb” , “7b. Angle sum property proof.ggb” , “7c. Angle sum property of a triangle.ggb”'''
3. Geogebra files : '''“7a. Angles in a right triangle.ggb” , “7b. Angle sum property proof.ggb” , “7c. Angle sum property of a triangle.ggb”'''
* '''How to do'''
* '''How to do'''
# Use the file - “7a. Angles in a right triangle.ggb”
# Use the file - “7a. Angles in a right triangle.ggb”
# Ask students what is the kind of triangle they observe.
# Ask students what is the kind of triangle they observe.
# Draw a parallel line to the side containing the right angle through the opposite vertex by dragging point D along the x-axis
# Draw a parallel line to the side containing the right angle through the opposite vertex by dragging point D along the x-axis
# Students should be able to recognize the corresponding angles formed when the parallel line is drawn.
# Students should be able to recognize the corresponding angles formed when the parallel line is drawn.
# Students should be able to recognize the alternate angles formed. Is the alternate angle same as one of the angles of the triangle.
# Students should be able to recognize the alternate angles formed. Is the alternate angle same as one of the angles of the triangle.
# So what can you say about the all the angles of the triangle?
# So what can you say about the all the angles of the triangle?
# With the file - “7b. Angle sum property proof.ggb”
# With the file - “7b. Angle sum property proof.ggb”
# Draw a line perpendicular to a side passing through the opposite vertex. How many triangles are formed. What kinds of triangles are formed?
# Draw a line perpendicular to a side passing through the opposite vertex. How many triangles are formed. What kinds of triangles are formed?
# In each of the two triangles if on angle is 90<sup>o</sup>, what will be the sum of the other two angles. What is the sum of these angles?
# In each of the two triangles if on angle is 90<sup>o</sup>, what will be the sum of the other two angles. What is the sum of these angles?
# Children can record the values of the angles of a triangle in the worksheet
# Children can record the values of the angles of a triangle in the worksheet
<nowiki>--------------</nowiki>
<nowiki>--------------</nowiki>
# With the file – “7c. Angle sum property of a triangle.ggb”
# With the file – “7c. Angle sum property of a triangle.ggb”
# Ask students what happens when the three angles of the triangle are placed adjacent to each other.
# Ask students what happens when the three angles of the triangle are placed adjacent to each other.
# What can you say about the line drawn?
# What can you say about the line drawn?
# Is it parallel to one of the sides?
# Is it parallel to one of the sides?
# What can you say about the pairs of angles – look at the matching colors.
# What can you say about the pairs of angles – look at the matching colors.
# Once the parallel line reaches the vertex, how many angles are formed?
# Once the parallel line reaches the vertex, how many angles are formed?
# Students should be able to identify the two angles moving are corresponding angles as the line moving is parallel to one of the sides.
# Students should be able to identify the two angles moving are corresponding angles as the line moving is parallel to one of the sides.
# Students can see that when the three angles of the triangle are placed adjacent to each other they form a straight line.
# Students can see that when the three angles of the triangle are placed adjacent to each other they form a straight line.
<nowiki>--------------</nowiki>
<nowiki>--------------</nowiki>
* Evaluation at the end of the activity
* Evaluation at the end of the activity
# Have students able to conclude if the sum of angles in any triangle is 180<sup>o</sup>?
# Have students able to conclude if the sum of angles in any triangle is 180<sup>o</sup>?
== Concept 4: Relation between interior and exterior angles in a triangle ==
== Concept 4: Relation between interior and exterior angles in a triangle ==
