Question: Exercise 2.1.8. Given triangle AABC, construct a parallel to BC at A. (How would we do this?) Use this construction to show that Playfair's Postulate

Exercise 2.1.8. Given triangle AABC, construct a parallel to BC at A. (How would we do this?) Use this construction to show that Playfair's Postulate (or Euclid's fifth) implies that the angle sum in a triangle is 180 degrees, namely, equal to two right angles. (The converse to this statement is also true: If the angle sum of a triangle is always 180 degrees, then Playfair's Postulate is true. For a proof see [41], [pages 21-23].)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Help me with this. Included Angel is the angel between two sides of a triangle Included side is the side common to two angles of a triangle NAME SCHOOL: SECTION DISTRICT: A. Readings/Discussions THE...

DIRECTIONS: For each of the following questions, you may only cite propositions 2.1, plane sepa- ration, line separation, and crossbar theorem; the incidence axioms, the betweenness axioms, and any...

If angle A is congruent to itself by the Reflexive Property, which transformation could be used to prove AABC ~ AADE by AA similarity postulate? D B E A O Translate triangle ABC so that point B lies...

== 1. Consider the Taxicab Model on R2 as defined in class. (See exercises 8.7 & 9.3) (a) Given AB, where A (1,0) and B (2, -1). and ray 1", where the ray is given by y = {x for x > 0 (origin point C...

Solve the triangle. For the sides, give an expression for the exact value of the length in terms of sine and approximate to 1 decimal place. B 330 C = 58 a 990 A b Part: 0 / 3 Part 1 of 3 b = sincos...

In class, we mentioned that (AAA) is a triangle congruence in a neutral geometry if and only if this neutral geometry is hyperbolic. Let's prove this result here. (a) First, we present a proof that,...

QUESTION 11 - 1 POINT What are the angles of AABC with side lengths a = 7, b = 9, and c = 10? Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining...

1 of 9 LYS Math 2412 - Final Exam Review Problems Update:11/18/ 1. Verify the identity: tan(x) sin(x) + cos(x) = sec(x) 2. Verify the identity: sin(x) - sin(x) cos2(x) = sin(x) 3. Verify the...

TOPIC: PROVING TRIANGLE CONGRUENCE TASK. FOR EACH OF THE FOLLOWING, ESTABLISH A TWO-COLUMN PROOF like in the smaples shown. there are examples below. thank you in advance. YOUR FINAL TASK TASK. For...

***Please answer in a two-column proof-statements and reasons, not paragraph (because it is way easier to understand). **Also, please have ONLY one given (statement) because a lot of it makes me...

Banya, Inc., just paid a dividend of $2.0 per share on its stock. The dividends are expected to grow at a constant rate of 4 percent per year, indefinitely. If investors require an 11 percent return...

This exercise is used in Section 13.6. Suppose that V is a nonempty, open set in R3 and that F: V R3 is C1. Prove that for each x0 V, where n is the outward-pointing normal of Br(x0). - limn F.nd

What is the BEST combination to perform QC on manitol salt agar

Julian Birkinshaw, James Manktelow, Vittorio DAmato, Elena Tosca, and Francesca Macchi In recent years, one of the most profound transformations in the workplace has been the increase in age...