illusiia

2020-11-08

Prove that the relation of congruence is an equivalence relation.

ensojadasH

Skilled2020-11-09Added 100 answers

Step 1

The definition of a congruence depends on the type of algebraic structure under consideration.

So, for the question “Prove that the relation of congruence is an equivalence relation.” we are taking in general.

Let$a\equiv b$ is denoted as a is congruent to b.

Step 2

Now,

Reflexive:

$Since\text{}a\text{}\equiv a\mathrm{\forall}a,\text{}the\text{}relation\text{}\equiv is\text{}reflexive$ .

Symmetry:

$Since\text{}a\equiv b\text{}then\text{}b\equiv \text{}a,the\text{}relation\text{}\equiv \text{}is\text{}symmetry$ .

Transitivity:

$Since\text{}a\equiv b\text{}and\text{}b\equiv c\text{}then\text{}a\equiv c\text{},\text{}the\text{}relation\text{}\equiv is\text{}transitive$ .

Hence, the relation of congruence is an equivalence relation.

The definition of a congruence depends on the type of algebraic structure under consideration.

So, for the question “Prove that the relation of congruence is an equivalence relation.” we are taking in general.

Let

Step 2

Now,

Reflexive:

Symmetry:

Transitivity:

Hence, the relation of congruence is an equivalence relation.

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

108,72What is the surface area to volume ratio of a sphere?

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

RectangleKaren says every equilateral triangle is acute. Is this true?

Find the number of lines of symmetry of a circle.

A. 0

B. 4

C. 2

D. InfiniteThe endpoints of a diameter of a circle are located at (5,9) and (11, 17). What is the equation of the circle?

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