Recent content by pholee95

I don't know how to start proving this theorem, so can someone please help? I need to prove that the circumcircles all intersect at a point M. Thank you! Miquel's Theorem: If triangleABC is any triangle, and points D, E, F are chosen in the interiors of the sides BC, AC, and AB, respectively...

Hi, I'm stuck on this problem and would like some help. The purpose of this exercise is to prove the Nine-Point Circle Theorem. Let triangleABC be a Euclidean triangle and let points D, E, F, L, M, N, and H be as in Figure 8.46. Let γ be the circumscribed circle for triangleDEF. a) Prove that...

I'm having a hard time proving that the Euclid Parallel Postulate is equivalent to this theorem. Can anyone please help? Euclid Parallel Postulate states: For every line l and point P not on l, there exists exactly one line m so that P is on m and m||l. the theorem states: (Proclus’s Axiom)...

Hello everyone. I need help on proofs. I have to proof the Angle-Angle-Side theorem. Can someone help me with this? The AAS states : If triangles ABC and DEF are two triangles such that angle ABC is congruent to angle DEF, angle BCA is congruent to angle EFD, and segment AC is congruent to DF...

Ah. I understand it now. Thank you so much for your help!

There are none right?

I'm stuck on this problem. Can anyone please help me understand? Consider the model of geometry where point means rational point in the Euclidean plane and all of our other terms have their normal interpretation. This model doesn't satisfy the Ruler Postulate because there isn't a one-to-one...

No it won't be the same. Right?

I'm not sure on how to do this problem. Can someone please help and explain? Thank you! Recall (Exercise 3.2.8) that the square metric distance between two points (x1, y1) and (x2, y2) in R^2 is given by D((x1, y1), (x2, y2))= max{|x2 − x1|, |y2 − y1|}. Show by example that R^2 with the square...