Difference between revisions of "Angle sum property"

Revision as of 10:56, 12 April 2019

Objectives

To establish the angle sum property of a triangle
To help visualization of the geometric proof

Estimated Time

Prerequisites/Instructions, prior preparations, if any

Prior understanding of point, lines and angles, adjacent angles, vertically opposite angles, linear pair, parallel lines, alternate angles, corresponding angles.

Materials/ Resources needed

Digital : Computer, geogebra application, projector.
Non digital : Worksheet and pencil.
Geogebra files :
1. “7a. Angles in a right triangle.ggb” ,
2. “7b. Angle sum property proof.ggb” ,
3. “7c. Angle sum property of a triangle.ggb”

Process (How to do the activity)

Use the file - “7a. Angles in a right triangle.ggb”
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
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.
So what can you say about the all the angles of the triangle?
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?
In each of the two triangles if on angle is 90^o, 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

Observation	Angle 1	Angle 2	Angle 3	Angle 1 + Angle 2 + Angle 3	What can you say about sum of angles?

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.
What can you say about the line drawn?
Is it parallel to one of the sides?
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?
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.

Evaluation at the end of the activity

Have students able to conclude if the sum of angles in any triangle is 180^o?

@@ Line 1: / Line 1: @@
-===Name of the activity===
+===Objectives===
-Brief blurb describing what the activity.  If this has been borrowed from some external web site (for example, a non OER or OER site which had this idea and based on which the activity was developed)
+*To establish the angle sum property of a triangle
+*To help visualization of the geometric proof
-=== Objectives ===
-Content objectives  - what content areas
-Skill objectives - what specific skills
-Classroom objectives - to demo peer learning, to make a classroom resource, etc -
-All these kinds of objectives need not be there for every activity.  And no need to list them as different headings.  This is only for our reference when we are developing activities.
 ===Estimated Time===
 === Prerequisites/Instructions, prior preparations, if any ===
+Prior understanding of point, lines and angles, adjacent angles, vertically opposite angles, linear pair, parallel lines, alternate angles,      corresponding angles.
 ===Materials/ Resources needed===
+*Digital : Computer, geogebra application, projector.
+*Non digital : Worksheet and pencil.
+*Geogebra files :
+*#'''“[https://ggbm.at/wjdsrz4w 7a. Angles in a right triangle.ggb]” ,'''
+*#'''“[https://ggbm.at/a2jjgpkn 7b. Angle sum property proof.ggb]” ,'''
+*#'''“[https://ggbm.at/fskbjzxj 7c. Angle sum property of a triangle.ggb]”'''
 ===Process (How to do the activity)===
-How to do the different steps of the activity?
+*Use the file - “[https://ggbm.at/wjdsrz4w 7a. Angles in a right triangle.ggb]”
+*Ask students what is the kind of triangle they observe.
-What kinds of questions you can ask for that activity
+*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.
-What are the student follow-up activities/ questions you can give?
+*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?
-Categories:  (Subject) (Topic) (Sub-concept/topic) (Class 6) (Resource format)
+*With the file - “[https://ggbm.at/a2jjgpkn 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?
-Example -  (Mathematics) (Triangle) (Area) (Perimeter) (Class 6) (Class 8) (Geogebra) (Video)
+*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
+{| class="wikitable"
+!Observation
+!Angle 1
+!Angle 2
+!Angle 3
+!Angle 1 + Angle 2 + Angle 3
+!What can you say about sum of angles?
+|-
+|
+|
+|
+|
+|
+|
+|-
+|
+|
+|
+|
+|
+|
+|-
+|
+|
+|
+|
+|
+|
+|}
+*With the file – “[https://ggbm.at/fskbjzxj 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.
+*What can you say about the line drawn?
+*Is it parallel to one of the sides?
+*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?
+*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.
+'''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>?