For the next few problems, suppose we are operating under Saccheri's Hypothesis of the Acute Angle (HAA). That is, we suppose that the congruent summit angles of any Saccheri Quadrilateral are acute. The thrust of these problems is to prove (1) that under HAA, triangles have fewer than 180° and (2) that under HAA the Pythagorean relationship between hypotenuse and legs of a right triangle cannot hold. This development is taken from Richard Trudeau's The Non-Euclidean Revolution. Under HAA, prove that if ABCD is a Saccheri Quadrilateral as shown, then AB -CD. A 23

For the next few problems, suppose we are operating under Saccheri's Hypothesis of the Acute Angle (HAA). That is, we suppose that the congruent summit angles of any Saccheri Quadrilateral are acute. The thrust of these problems is to prove (1) that under HAA, triangles have fewer than 180° and (2) that under HAA the Pythagorean relationship between hypotenuse and legs of a right triangle cannot hold. This development is taken from Richard Trudeau's The Non-Euclidean Revolution. Under HAA, prove that if ABCD is a Saccheri Quadrilateral as shown, then AB -CD. A 23

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 39E: The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of...

See similar textbooks

Similar questions

Solve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. Points A, B, C, D, and E are tangent points. a. If AB=46.00 and DE=66.00 , find 1. b. If AB=53.00 and DE=70.00 , find 1.
Given: Tangents AB,BC,andACtoO at points M, N, and P, respectively. AB=14,BC=16,AC=12 Find: AM, PC, and BN
For the 30-60-90 triangle shown, suppose that XY=2a. Find: a XZ b YZ
An auto parts dealer in Huntsville, Alabama at point H, has called a manufacturer for parts needed as soon as possible. The dealer will, in fact, send a courier for the necessary equipment. The manufacturer has two distribution centers located in nearby Tennessee-one in Nashville at point N and the other in Jackson at point J. Using the angle measurements indicated on the accompanying map, determine to which town the courier should be dispatched to obtain the needed parts
The larger circle is inscribed in a square with sides of length 4cm. The smaller circle is tangent to the larger circle and to two sides of the square, as shown. Find the length of the radius of the smaller circle.
The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
What relationship, if any, exists between two angles a with equal measures? b that have the same vertex and a common side between them?
For coplanar points A,B, and C, suppose that you have used the Distance Formula to show that AB=5,BC=10, and AC=15. What can you conclude regarding points A,B, and C?
The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.