![](https://cdn.geogebra.org/resource/jdbtqs25/rbnPY2Z6WV2Wzsed/material-jdbtqs25.png)
שטחי משולשים בין מקבילים
move points C and D. what happens to the area?
חוצה זוית פנימית וחוצה זוית חיצונית
מטלת השתלמות, גאומטריה עמט ט
ב1 עמוד 297 תרגיל 7
Use the scroll bar to unfold the problem.[br]Do you have a conjecture?[br]Try to prove it![br][br]השתמשו בסרגל הגלילה לגילוי שלבי הבעייה[br]האם יש לכם השערה? נסו להוכיח
tangential quadrilateral
Ptolemy and Cyclic Quadrilaterals
Prove that the product of the diagonals is the sum of the product of the pairs of opposite sides
Proof:
1. Explain the construction[br]2. Prove that the triangles in the first pair are similar. [br]3. Prove that the triangles in the second pair are similar.[br]4. Write out the proportions deduced from the above steps [br]5. Finish the proof[br](solution at the bottom of this page)
And what does this theorem say when the quadrilateral is a rectangle?
spoilers:
[math]\frac{AD}{EC}=\frac{BD}{BC}[/math] and therefore [math]AD\cdot BC=BD\cdot EC[/math][br][br][math]\frac{AE}{CD}=\frac{AB}{BD}[/math] and therefore [math]AB\cdot CD=AE\cdot BD[/math][br][br]adding both equations we get [math]AB\cdot CD+AD\cdot BC=\left(AE+EC\right)BD=AC\cdot BD[/math]
קטע אמצעים בטרפז 1
מרחק בין נקודות
![](https://cdn.geogebra.org/resource/jdbtqs25/rbnPY2Z6WV2Wzsed/material-jdbtqs25.png)
.
![](https://cdn.geogebra.org/resource/sgxfdhbb/rNscpXIHjvd2kehl/material-sgxfdhbb.png)
![](https://cdn.geogebra.org/resource/vthqemtx/EMbHW3NOL4O6ZFQZ/material-vthqemtx.png)
images taken from [url=https://www.google.com/url?sa=i&source=imgres&cd=&cad=rja&uact=8&ved=2ahUKEwik4fr648XkAhWJzKQKHcFKCXEQjB16BAgBEAM&url=https%3A%2F%2Fwww.physics.utoronto.ca%2F~jharlow%2Fteaching%2Fastrophys03%2Fgeodesic.html&psig=AOvVaw3FbI1jI4KtRnSpXWVHKKXu&ust=1568188033726452]here[/url][br]and [url=https://gisgeography.com/great-circle-geodesic-line-shortest-flight-path/]here[/url] (GISGeography)