Difference between revisions of "Sum of the interior angles of a quadrilateral"

From Karnataka Open Educational Resources
Jump to navigation Jump to search
 
(13 intermediate revisions by one other user not shown)
Line 1: Line 1:
 +
The sum of the measures of the angles in any quadrilateral is 4 right angles.
  
 
=== Objectives ===
 
=== Objectives ===
−
# To establish that sum of interior angles of any quadrilateral is 360<sup>o</sup>
+
To establish that sum of interior angles of any quadrilateral is 360°
−
 
 
 
===Estimated Time===
 
===Estimated Time===
 
40 minutes
 
40 minutes
Line 13: Line 13:
 
* Non digital : Worksheet and pencil
 
* Non digital : Worksheet and pencil
 
* Geogebra files : ‘[https://ggbm.at/dseaa3pq Sum of the interior angles of a quadrilateral.ggb]’
 
* Geogebra files : ‘[https://ggbm.at/dseaa3pq Sum of the interior angles of a quadrilateral.ggb]’
 +
 +
{{Geogebra|dseaa3pq}}
  
 
===Process (How to do the activity)===
 
===Process (How to do the activity)===
 
* In the geogebra sketch for the quadrilateral measure the sides and angles at the vertices
 
* In the geogebra sketch for the quadrilateral measure the sides and angles at the vertices
 
* Calculate the sum of these angles of the quadrilateral? Note your observations
 
* Calculate the sum of these angles of the quadrilateral? Note your observations
−
*  {| class="wikitable" |Quadrilateral |Side1 |Side2 |Side3 |Side4 |Angle1 |Angle2 |Angle3 |Angle4 |Angle1+Angle 2+ Angle3 + Angle 4 |Whatdo you observe about their sum |- |Q1 | | | | | | | | | | |- |Q2 | | | | | | | | | | |- |Q3 | | | | | | | | | | |}
+
{| class="wikitable"
−
 
+
|Quadrilateral
 +
|Side1
 +
|Side2
 +
|Side3
 +
|Side4
 +
|Angle1
 +
|Angle2
 +
|Angle3
 +
|Angle4
 +
|Angle1+Angle 2+ Angle3 + Angle 4
 +
|Whatdo you observe about their sum
 +
|-
 +
|Q1
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
|Q2
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
|Q3
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|}
 
* Draw any one diagonal. What do you notice? What is the quadrilateral divided into? How many triangles are formed?
 
* Draw any one diagonal. What do you notice? What is the quadrilateral divided into? How many triangles are formed?
 
* What is the measure of the sum of angles in each quadrilateral? So what is the measure of all the angles of the quadrilateral?
 
* What is the measure of the sum of angles in each quadrilateral? So what is the measure of all the angles of the quadrilateral?
 
* Make different quadrilaterals. Divide it into two triangles, measure the angles of the two triangles, check their sum.
 
* Make different quadrilaterals. Divide it into two triangles, measure the angles of the two triangles, check their sum.
−
* Tabulate the angles of the two triangles  {| class="wikitable" |Observation | colspan="4" |Triangle1 | colspan="4" |Triangle2 |Sum of angles of two triangle Triangle1 + Triangle2 |- | |Angle 1 |Angle 2 | Angle 3 |Sum of angles |Angle 1 |Angle 2 | Angle 3 |Sum of angles | |- |Q1 | | | | | | | | | |- |Q2 | | | | | | | | | |- |Q3 | | | | | | | | | |}
+
* Tabulate the angles of the two triangles 
 +
{| class="wikitable"
 +
|Observation
 +
| colspan="4" |Triangle1
 +
| colspan="4" |Triangle2
 +
|Sum of angles of two triangle
 +
|-
 +
|
 +
|Angle 1
 +
|Angle 2
 +
|
 +
Angle 3
 +
|Sum of angles
 +
|Angle 1
 +
|Angle 2
 +
|
 +
Angle 3
 +
|Sum of angles
 +
|
 +
|-
 +
|Q1
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
|Q2
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
|Q3
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|}
 +
 
 +
'''Evaluation at the end of the activity'''
 +
* Is the sum of all angles in any quadrilateral 360<sup>o</sup>.
 +
 
 +
[[Category:Quadrilaterals]]

Latest revision as of 07:33, 7 November 2019

The sum of the measures of the angles in any quadrilateral is 4 right angles.

Objectives

To establish that sum of interior angles of any quadrilateral is 360°

Estimated Time

40 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles, intersecting lines, vertically opposite angles, properties of triangle

Materials/ Resources needed


Download this geogebra file from this link.


Process (How to do the activity)

  • In the geogebra sketch for the quadrilateral measure the sides and angles at the vertices
  • Calculate the sum of these angles of the quadrilateral? Note your observations
Quadrilateral Side1 Side2 Side3 Side4 Angle1 Angle2 Angle3 Angle4 Angle1+Angle 2+ Angle3 + Angle 4 Whatdo you observe about their sum
Q1
Q2
Q3
  • Draw any one diagonal. What do you notice? What is the quadrilateral divided into? How many triangles are formed?
  • What is the measure of the sum of angles in each quadrilateral? So what is the measure of all the angles of the quadrilateral?
  • Make different quadrilaterals. Divide it into two triangles, measure the angles of the two triangles, check their sum.
  • Tabulate the angles of the two triangles 
Observation Triangle1 Triangle2 Sum of angles of two triangle
Angle 1 Angle 2

Angle 3

Sum of angles Angle 1 Angle 2

Angle 3

Sum of angles
Q1
Q2
Q3

Evaluation at the end of the activity

  • Is the sum of all angles in any quadrilateral 360o.
Retrieved from "https://karnatakaeducation.org.in/KOER/en/index.php?title=Sum_of_the_interior_angles_of_a_quadrilateral&oldid=32522"