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Basic Proportionality Theorem (Thales theorem): If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio.In ∆ABC , if DE || BC and intersects AB in D and AC in E then AD AE ---- = ------ DB EC |
1) EF ┴ BA | 1) Construction |
2) EF is the height of ∆ADE and ∆DBE | 2) Definition of perpendicular |
3)Area(∆ADE) = (AD .EF)/2 | 3)Area = (Base .height)/2 |
4)Area(∆DBE) =(DB.EF)/2 | 4) Area = (Base .height)/2 |
5)(Area(∆ADE))/(Area(∆DBE)) = AD/DB | 5) Divide (4) by (5) |
6) (Area(∆ADE))/(Area(∆DEC)) = AE/EC | 6) Same as above |
7) ∆DBE ~∆DEC | 7) Both the ∆s are on the same base and between the same || lines. |
8) Area(∆DBE)=area(∆DEC) | 8) If the two triangles are similar their areas are equal |
9) AD/DB =AE/EC | 9) From (5) and (6) and (7) |
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.