Question

Prove the Vertical Angle Theorem. Please state why and construct a proof!

Answer #1

Prove the HL Theorem without angle measures
or Pythagorean theorem. cannot
include HL theorem in proof

Using the hyperbolic angle sum theorem, prove theorem 1. theorem
1 (the exterior angle inequality theorem): An exterior angle of a
triangle is greater than each of the remote/nonadjacent interior
angles of the triangle. hyperbolic angle sum theorem: The sum of
the measures of the angles of a hyperbolic triangle is less than
180°. Please give an original answer, the explanations already
posted on Chegg do not answer this question or do not answer in a
language that I understand...

Prove the angle subtraction theorem

prove HL Theorem without angle measure.

4. State and prove the Taylor’s Theorem.

State and prove the Generalised Rolle’s theorem.

Assuming Playfair’s axiom. Prove the Alternate interior angle
theorem and that the sum of the interior angles if a triangle is
180. Use these results to solve problems. Please show your work and
explanations.

1. Prove Thales’ Theorem: In a circle, if ∠ABC is an
inscribed angle and AC is a diameter, then
∠ABC is a right angle.

Prove that f(x)=x*cos(1/x) is continuous at x=0.
please give detailed proof. i guess we can use squeeze
theorem.

Heine-Borel Theorem.
a. State the Heine-Borel Theorem
b. Assume A ⊆ R and B ⊆ R . Prove using only the definition of
an open set that if A and B are open sets then A∩ B is an open
set.
c. Assume C ⊆ R and D ⊆ R . Prove that if C and D are compact
then C ∪ D is compact. There are two methods: Using the definition
of compact or a proof that uses parts...

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