Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. in this multi-part exercise, we'll prove another r

In this multi-part exercise, we'll prove another result alluded to in class, namely that if the...

70.2K

Verified Solution

Question

Basic Math

In this multi-part exercise, we'll prove another result alludedto in class, namely that if the Pythagorean theorem holds in aneutral geometry, then the geometry is Euclidean. So, assume thePythagorean theorem holds. Let ABC be an isosceles right triangle,with right angle at C and sides AC and BC equal. Let CM denote thealtitude from C to the hypotenuse AB.

(a) Explain why M is the midpoint of AB.

(b) Prove that CM = AM (which, from part (a), is also equal toMB). Remember, we're assuming the Pythagorean theorem here.

(c) Use the result of part (b), and some angle-chasing, to provethat the sum of the angles of ABC is 180 degrees.

(d) Explain in one sentence why part (c) shows that the geometryis Euclidean.

Answer & Explanation Solved by verified expert
3.8 Ratings (558 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Biology
1.2K views

Grazing animals such as bison and burrowing animals such as prairie dogs are common animals...

Basic Math
1.2K views

La Jolla Beverage Products is considering producing a wine cooler that would be a blend of...

Biology
1.2K views

What process results in the removal of the glucosyl residue from the nonreducing end of the...

Basic Math
1.2K views

1. A company is testing how different compensation plans might affect a salespersons performance. The company...

Geometry
1.2K views

Find a plane containing the line lx t 5 4ty t 6 5t z t...

Calculus
1.2K views

An apple farm yields an average of 41 bushels of apples per tree when 25...

Algebra
1.2K views

Graph the following function 6 if 0 x 2 12 if 2 x 4 18...

Accounting
1.2K views

Forest Components makes aircraft parts. The following transactions occurred in July. ...

Accounting
1.2K views

Cheng and Morales, zwo recent graduates of Upper State University, formed a computer consulting firm....

Accounting
1.2K views

TB MC Qu. 7-87 (Static) The following data have been provided... The following data...

Accounting
1.2K views

Detmer Enterprises has budgeted sales for the next three months as follows: Budgeted Sales in...

Finance
1.2K views

Congratulations! Your portfolio returned 12.7% last year, 1.9% better than the market return of 10.8%....