Given triangle ABC, use the axioms to construct a fourth point D so that Triangle ABD is congruent, but not equal to Triangle ABC. State the axioms that you use in your construction. Which axiom implies that the triangle are congruent? Here is a list of the axioms: Axiom 1 (The Point-Line Incidence Axiom). A line is a set of points. Given any two differentpoints, there is exactly one line that contains them.Axiom 2 (The Ruler Axiom).1. For any two points A and B, there is a positive numbercalled the distance from A to B and denoted AB.2. For each line L, there is a function ƒ that assigns a real number to each point of L in sucha way that:(a) Different points have different numbers associated with them.(b) Every number – positive, negative, or zero- has some point with which it is associated.(c) If A and B are points of L, then |f(B) – f(A)| = AB, the distance from A to B. Notethat if A and B designate the same point, then AB = 0.%3DAxiom 3 (Pasch's Separation Axiom for a Line). Given a line L in the plane, the points in theplane that are not on L form two non-empty sets, H1 and H2, called half-planes, so:1. If A and B are points in the same half-plane, then AB lies wholly in that half-plane.2. If A and B are points not in the same half-plane, then AB intersects L.Axiom 4 (The Angle Measurement Axiom). To every angle, there corresponds a real numberbetween 0° and 180° called its measure or size. We denote the measure of ZBAC by MZBAC.Axiom 5 (The Angle Construction Axiom). Let AB lie entirely on the boundary line L of somehalf-plane H. For every number r where 0° Axiom 7 (The Supplementary Angles Axiom). If two angles are supplementary, then their mea-sures add to 180°.Axiom 8 (The Side-Angle-Side (SAS) Congruence Axiom). Suppose we have triangles ABC andA'B'C", where some or all of the vertices of the second triangle might be vertices of the firsttriangle as well. If1. mZA= mZA', and2. AB = A'B' and AC = A'C",then the triangles are congruent and the correspondence is: A → A', B –→ B', C → C'.Axiom 9 (Euclid's Parallel Axiom). Given a point P off a line L, there is at most one line in theplane through P not meeting L.

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Answered: construct a fourth point D so that…

Math

Algebra

construct a fourth point D so that Triangle

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 4AEXP

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