logging in or signing up Maths_AA3 choykw Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 25 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: April 24, 2010 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Slide 1: Produced by: Tan Yan Kert (28) Leader Emmanuel Lee (9) Assistant Leader Samuel Choy (23) Resource Person Sum of Interior Angles in a Triangle Slide 2: It is known that the interior angles of a triangle always add up to 180°. What are the reasons that it works? As such, our group has done research on it and we are going to present our results. Introduction : Introduction The Greek mathematician, Euclid, was the first to prove that the angles in the triangle is 180 degrees. However, the angles in a triangle on a sphere is not 180 degrees. The angles in a triangle will only be 180 degrees when the triangle is drawn on a flat surface. Reason 1 : Reason 1 As we know, the angle sum of a polygon with sides is 180(n-2). For example, a pentagon has 5 sides, so the sum of its interior angle is 180(3)=540 degrees. The sum of the angles of a triangle also has the same idea. The triangle has three sides. So the sum of it’s interior angles is 180(3-1) = 180(1) = 180. Reason 2: : Reason 2: a b c D E Firstly draw a line AB parallel to line DE. The value of ACD would be the same as CDE while the value of BCE would be the same as CED. This is because they are all alternate angles (AB//DE). They would then form a 180° angle. This shows that the interior angles in a triangle add up to 180°. Slide 6: Reason 3: a b c c A B D F G Firstly, draw a straight line CE parallel to line FG Next, extend lines FD and GD. The value of ADC would be the same as DGF while the value of DFG would be the same as BDE. This is because they are all corresponding angles The value of ADB is the same as FDG as they are vertically opposite angles They would form a 180° angle and this shows that the interior angles in a triangle add up to 180° Reason 4: : Reason 4: Firstly, make a duplicate of the triangle ACD. Put it beside the original triangle. A B C D E The value of ADB would be the same as the value of CAD. This is because they are all alternate angles (AC//BD). They would form a 180° angle. This proves that the interior angles in a triangle add up to 180°. Slide 8: Reason 5: Firstly, make a duplicate of the triangle ABC. A B C D A quardiletral would be formed when the 2 triangles are joined together. As the sum of angles in a quardiletral is 360°, the angles in one of the triangle would add up to 180°. Sources : Sources www.youtube.com/watch?v=f3mf5s3_mvq www.algebralab.org/lessons/lesson.aspx?file=Geometry_TrianglesSumangles.xml http://math4allages.wordpress.com/tag/triangle-angle-sum/ http://www.cut-the-knot.org/triangle/pythpar/AnglesInTriangle.shtml Thank You!!!Done by:Tan Yan Kert (leader)Emmanuel Lee (Assistant leader)Samuel Choy (Resource Person) : Thank You!!!Done by:Tan Yan Kert (leader)Emmanuel Lee (Assistant leader)Samuel Choy (Resource Person) You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Maths_AA3 choykw Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 25 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: April 24, 2010 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Slide 1: Produced by: Tan Yan Kert (28) Leader Emmanuel Lee (9) Assistant Leader Samuel Choy (23) Resource Person Sum of Interior Angles in a Triangle Slide 2: It is known that the interior angles of a triangle always add up to 180°. What are the reasons that it works? As such, our group has done research on it and we are going to present our results. Introduction : Introduction The Greek mathematician, Euclid, was the first to prove that the angles in the triangle is 180 degrees. However, the angles in a triangle on a sphere is not 180 degrees. The angles in a triangle will only be 180 degrees when the triangle is drawn on a flat surface. Reason 1 : Reason 1 As we know, the angle sum of a polygon with sides is 180(n-2). For example, a pentagon has 5 sides, so the sum of its interior angle is 180(3)=540 degrees. The sum of the angles of a triangle also has the same idea. The triangle has three sides. So the sum of it’s interior angles is 180(3-1) = 180(1) = 180. Reason 2: : Reason 2: a b c D E Firstly draw a line AB parallel to line DE. The value of ACD would be the same as CDE while the value of BCE would be the same as CED. This is because they are all alternate angles (AB//DE). They would then form a 180° angle. This shows that the interior angles in a triangle add up to 180°. Slide 6: Reason 3: a b c c A B D F G Firstly, draw a straight line CE parallel to line FG Next, extend lines FD and GD. The value of ADC would be the same as DGF while the value of DFG would be the same as BDE. This is because they are all corresponding angles The value of ADB is the same as FDG as they are vertically opposite angles They would form a 180° angle and this shows that the interior angles in a triangle add up to 180° Reason 4: : Reason 4: Firstly, make a duplicate of the triangle ACD. Put it beside the original triangle. A B C D E The value of ADB would be the same as the value of CAD. This is because they are all alternate angles (AC//BD). They would form a 180° angle. This proves that the interior angles in a triangle add up to 180°. Slide 8: Reason 5: Firstly, make a duplicate of the triangle ABC. A B C D A quardiletral would be formed when the 2 triangles are joined together. As the sum of angles in a quardiletral is 360°, the angles in one of the triangle would add up to 180°. Sources : Sources www.youtube.com/watch?v=f3mf5s3_mvq www.algebralab.org/lessons/lesson.aspx?file=Geometry_TrianglesSumangles.xml http://math4allages.wordpress.com/tag/triangle-angle-sum/ http://www.cut-the-knot.org/triangle/pythpar/AnglesInTriangle.shtml Thank You!!!Done by:Tan Yan Kert (leader)Emmanuel Lee (Assistant leader)Samuel Choy (Resource Person) : Thank You!!!Done by:Tan Yan Kert (leader)Emmanuel Lee (Assistant leader)Samuel Choy (Resource Person)