Question

Describe how geometric quantities are identified as being equal.

Describe how the coordinate plane is used in studying geometry.

Answer 1

How geometric quantities are identified as being equal-

Two figures are identified as equal if they are of same shape and of same size .They are also called as ''congruent' means of same shape and same size.

For example-

Two circles of same raddi are equal.

Two squares of same side are equal.

Two triangles of same corrosponding sides and same corrosponding angles are equal.

Let us understand it more clearly by the congruence of two triangles.

The two given in the triangle's are equal if they satisfy any of these rule-

SAS ( SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.),

ASA( angle,side,angle) congruence,

AAS(angle,angle,side) congruence, etc

So in this way two figures or quantities are identified as equal if their shape and size are equal.

How the coordinate plane is used in studying geometry-

Coordinate plane is used to locate the position of an object or a point.For this we require two perpendicular lines. One of them is horizontal and one is vertical.

The horizontal line is called x axis and vertical line is called y axis.

For example as shown if we have 3 points in the plane. Then on joing the points,we get a triangle. Now if we know the coordinate of these pints then we can find anything about the triangle- length of its sides, angles, area of the triangle etc.

Similarly other figure can be represent on the coordinate plane and information about them can be calculated by using some formulas.

So in this way coordinate plane is useful in studying geometry.