Why your proof does not rely on the parallel postulate

Assignment Help Other Subject

Reference no: EM133794167

Problem: Using Euclid's Element

I. (The Alternate Interior Angle Theorem I.27). Given lines MN and JK, suppose that line PQ intersects MN at point X and line JK intersects PQ at point Y. Given that ∠MXY ? ∠XYK, prove that line MN is parallel to JK. Include a diagram using these labels. For your proof, give a step by step argument. You may cite any proposition up to and including I.26, definition, postulate, or common notion from Elements as a valid reason. Briefly explain why your proof does not rely on the parallel postulate.

II. (Converse of the Alternate Interior Angle Theorem I.29). Given lines MN and JK, suppose that line PQ intersects MN at point X and line JK intersects PQ at point Y. Given that MN is parallel to JK, prove that ∠MXY ? ∠XYK. Include a diagram using these labels. For your proof, give a step by step argument. You may cite any proposition up to and including I.28, definition, postulate, or common notion from Elements as a valid reason. Briefly explain why your proof does rely on the parallel postulate.

Reference no: EM133794167

Questions Cloud

What stands out to you and what might explain any difference : Compare the leading causes in the early 1900s to the mid-1900s, and then to present day. What stands out to you and what might explain any differences?

Experiencing pain and difficulty respiration : A patient is terminally ill and experiencing pain and difficulty respiration. Discuss the physiological presentation and signs and symptoms associated

What were the most important factors that led to the fire : What were the most important factors that led to the fire and loss of lives as described in your assigned book?

Nonsteroidal anti-inflammatory medications : A patient has osteoarthritis and has been instructed to take nonsteroidal anti-inflammatory medications.

Why your proof does not rely on the parallel postulate : Given lines MN and JK, suppose that line PQ intersects MN at point X and line JK intersects. Briefly explain why your proof does not rely on parallel postulate.

Custom-designed landscaping for residential areas : Joan's Nursery specializes in custom-designed landscaping for residential areas. Labor costs of planting trees are important to the nursery

Preferences are considered in evidence-based practice : Patients and their personal values and preferences are considered in evidence-based practice.

What is the best compromise position : What's the best compromise position? Ultimately, this is the most important question for sports policymakers in this period.

Piercing abdominal pain and elevated serum amylase : A client with acute pancreatitis is admitted with severe, piercing abdominal pain and an elevated serum amylase.

User Account

All Pages