Tara Alvarado

2021-12-13

Let $Q}^{2$ be the rational plane of all ordered pairs (x,y) of rational numbers with the usual interpretations of the undefined geometric terms used in analytical geometry. Show that axiom C-1 and the elementary continuity principle fail in $Q}^{2$ . (Hint: the segment from (0,0) to (1,1) can not be laid off on the x axis from the origin.

Axiom C-1: If A, B are two points on a line a, and if A' is a point upon the same or another line a′ , then, upon a given side of A′ on the straight line a′ , we can always find a point B′ so that the segment AB is congruent to the segment A′B′ . We indicate this relation by writing$AB\stackrel{\sim}{=}A\prime B\prime$ . Every segment is congruent to itself; that is, we always have $AB\stackrel{\sim}{=}AB$ .

Axiom C-1: If A, B are two points on a line a, and if A' is a point upon the same or another line a′ , then, upon a given side of A′ on the straight line a′ , we can always find a point B′ so that the segment AB is congruent to the segment A′B′ . We indicate this relation by writing

sonSnubsreose6v

Beginner2021-12-14Added 21 answers

Step 1

Let A, B lies on Horizontal axis.

Lets

Let A, B lies on Horizontal axis.

Lets

scoollato7o

Beginner2021-12-15Added 26 answers

Suppose that the Elementary Continuity Principle holds for this interpretation. Let

Let C be the circle in

Since

Since Q lies on

The distance between the centers of two circles C1 and C2 is equal to 10 cm. The circles have equal radii of 10 cm.

A part of circumference of a circle is called

A. Radius

B. Segment

C. Arc

D. SectorThe perimeter of a basketball court is 108 meters and the length is 6 meters longer than twice the width. What are the length and width?

What are the coordinates of the center and the length of the radius of the circle represented by the equation ${x}^{2}+{y}^{2}-4x+8y+11=0$?

Which of the following pairs of angles are supplementary?

128,62

113,47

154,36

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An angle which measures 89 degrees is a/an _____.

right angle

acute angle

obtuse angle

straight angleHerman drew a 4 sided figure which had only one pair of parallel sides. What could this figure be?

Trapezium

Parallelogram

Square

RectangleWhich quadrilateral has: All sides equal, and opposite angles equal?

Trapezium

Rhombus

Kite

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Find the number of lines of symmetry of a circle.

A. 0

B. 4

C. 2

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What is the number of lines of symmetry in a scalene triangle?

A. 0

B. 1

C. 2

D. 3How many diagonals does a rectangle has?

A quadrilateral whose diagonals are unequal, perpendicular and bisect each other is called a.

A. rhombus

B. trapezium

C. parallelogram