Desargues' theorem states that two triangles are in perspective axially if and only if they are in perspective centrally. Corresponding sides of the triangles, when extended, meet at points on a line called the axis of perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of perspectivity. Desargues's theorem states that the truth of the first condition is necessary and sufficient for the truth of the second.
Use the following applet produced in GeoGebra to play around the with the points on the lines to see Desargues's theorem in action.
Let's try Desargues's Theorem with Level 5 Dobble!
Drag the cards from the cards containers into the circles(points) on the lines and triangles.
You can click on a symbol(letter) to highlight the cards that contains the chosen symbol and click on two symbols to highlight the card that contains both of those symbols. Similarly, you can click on a card to highlight the symbols that the card conatins and click on two cards to highlight the symbol that the both of those cards contains.
If the three cards on a line has a common symbol, the symbol will be shown next to the line to verify you have chosen the right cards to form the line, indicating that you are in the right path.
Happy Desargues-Dobble playing!
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SYMBOLS: