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THE ANGLES AND AREA OF A TRIANGLE |
| Geometry | |
| 1. THE SUM OF THE ANGLES IN A TRIANGLE | ||
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The sum of the angles in any triangle is always the same as two right angles (180º). Use the following Descartes window to draw a triangle where point A is fixed and points B and C can move, although B can only move horizontally. The line that passes through point C is parallel to AB and has been drawn to indicate that the three angles in any triangle always add up to 180º. The green angles are equal as they are interior alternate angles, as are the two yellow ones. If we add angle C to these other two angles we get a straight angle, whatever the triangle is that is constructed. |
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| 1.- Draw
triangles with the following sides and angles:
a) A=90º, AB=4 y AC=3 b) B=90º, AB=4, A=45º c) AB=3, B=120º, A=30º.
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| 2. THE AREA OF ANY TRIANGLE | |
| We know that the area of a triangle is equal to half of its base multiplied by its height. Let's see why. In the following Descartes window the triangle ABC is the same as the triangle AB' C as its respective sides are parallel. The two triangles form the parallelogram ABCB' and therefore the area of the triangle ABC is half of that of the parallelogram. As the area of a parallelogram is equal to its base multiplied by its height, the area of the triangle is half of the area of its base multiplied by its height. | |
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2.-
Draw
a right-angled triangle (A=90º) whose base AB = 4 and height = 3. Work
out the area of the triangle. 3.- Can you explain why the area of a triangle is half of its base multiplied by its height? 4.- What is the area of triangles with the same base and height? In other words, triangles formed by moving point C horizontally. |
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| Miguel García Reyes | ||
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| Spanish Ministry of Education. Year 2001 | ||
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