Let A and B be not on the same side of CD. Let AB cuts CD at F.
As ABCD is a Saccheri quadrilateral so BAD =90? and CDA=90?. Now one of the triangles DAF and BFC contains a right angle and an obtuse angle because one of the linear pair of angles of F must be an obtuse or a right angle. In this case, angles FAD=90? and FDA=90?. As a result of which, the sum of the three angles of a triangle will be more than 180?. Contradiction!!!! Hence A and B must lie on the same side of CD
Let C and D be not on the same side of AB. Let CD cuts AB at E.
As ABCD is a Saccheri quadrilateral so BAD =90? and CDA=90?. Now one of the triangles DAE and BEC contains a right angle and an obtuse angle because one of the linear pair of angles of E must be an obtuse or a right angle. In this case angles EAD=90? and EDA=90?. So sum of three angles in Triangle EAD is more than 180?. Contradiction!!!!
Hence C and D must lie on the same side of AB
Let A and D be not on the same side of BC. Let AD cuts BC at F.
As ABCD is a Saccheri quadrilateral so BAD =90? and CDA=90?. Now one of the triangles DCF and BAF contains a right angle and an obtuse angle because one of the linear pair of angles of F must be an obtuse or a right angle. In this case angles FDC=90? and CFD≥90?. So sum of three angles in Triangle CDF is more than 180?. Contradiction!!!! Hence A and D must lie on the same side of BC.
Essay Writing Service Features
Our Experience
No matter how complex your assignment is, we can find the right professional for your specific task. Contact Essay is an essay writing company that hires only the smartest minds to help you with your projects. Our expertise allows us to provide students with high-quality academic writing, editing & proofreading services.
Free Features
Free revision policy
$10Free bibliography & reference
$8Free title page
$8Free formatting
$8How Our Essay Writing Service Works
First, you will need to complete an order form. It's not difficult but, in case there is anything you find not to be clear, you may always call us so that we can guide you through it. On the order form, you will need to include some basic information concerning your order: subject, topic, number of pages, etc. We also encourage our clients to upload any relevant information or sources that will help.
Complete the order form
Once we have all the information and instructions that we need, we select the most suitable writer for your assignment. While everything seems to be clear, the writer, who has complete knowledge of the subject, may need clarification from you. It is at that point that you would receive a call or email from us.
Writer’s assignment
As soon as the writer has finished, it will be delivered both to the website and to your email address so that you will not miss it. If your deadline is close at hand, we will place a call to you to make sure that you receive the paper on time.
Completing the order and download