Introduction for meaning of geometry:
The word “geometry” is derived from grouping of two Greek words “Geo” and “me tron”. The word “Geo” means “earth” and “me tron” means “measurement”. So the subject name is “earth measurement” . It was originally named as “geometry”.
Geometry is one of the main branch of mathematics, which involves the study of shapes, line equation, angles, and dimensions, relative position of diagrams etc. The basic diagram of geometry is point, line, square, rectangle, triangle, and circle. The geometry properties and example problems are given below.
Let us see properties and theorems of geometry meaning. And also see solved example problems using geometry meaning. I like to share this Ray Geometry with you all through my article.
Properties and theorems for geometry:
Property 1: If any two points on a plane, there is one and only one line containing them.
Property 2: Two distinct lines cannot have more than one point in common
Property 3: If a line and a point not on it, there is one and only one line that passes through the given point and is parallel to the given line.
Property 4: If the given two lines intersect, then the vertically opposite angles are equal.
Property 5: If a given transversal intersects two parallel lines, then any pair of corresponding angles are equal.
Property 6: If any two sides and the included angle of one triangle are equal to any two sides and the included angle of another triangle, then the two triangles are congruent
Theorem 1:
The given two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle.
Draw a triangle ABC and a line XY parallel to the side BC (see Figure). Mark the point of intersection of line XY and the side AB as D, and the point of intersection of the line XY and the side AC as E. Since the side AB and the side AC are transversal of the parallel line segments XY and BC,
∠D = ∠B, ∠E = ∠C
The two triangles ABC and ADE have AAA property. However, they are not congruent since the corresponding sides are not equal. Hence, we conclude that AAA correspondence cannot be a criterion for congruency of triangles.
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Example Problems - Geometry:
Example problem 1:
Find the supplement of the following angles:
(i) 70° (ii) 45° (iii) 120° (iv) 155°
Solution:
Since the sum of supplementary angles is 180°,
(i) the supplement of 70° is 180° − 70° = 110°.
(ii) the supplement of 45° is 180° − 45° = 135°.
(iii) the supplement of 120° is 180° − 120° = 60°.
(iv) the supplement of 155° is 180° − 155° = 25°.
Example problem 2:
If the angles of a triangle are in the ratio 4 : 4 : 7, find them.
Solution:
Let the angles be 4x, 4x, 7x.
Then 4x + 4x + 7x = 180° or 15x = 180° or x = 12°.
The angles are 4 × 12°, 4 × 12°, 7 × 12°, or 48°, 48°, 84°.
This is how problems solved using geometry meaning.
The word “geometry” is derived from grouping of two Greek words “Geo” and “me tron”. The word “Geo” means “earth” and “me tron” means “measurement”. So the subject name is “earth measurement” . It was originally named as “geometry”.
Geometry is one of the main branch of mathematics, which involves the study of shapes, line equation, angles, and dimensions, relative position of diagrams etc. The basic diagram of geometry is point, line, square, rectangle, triangle, and circle. The geometry properties and example problems are given below.
Let us see properties and theorems of geometry meaning. And also see solved example problems using geometry meaning. I like to share this Ray Geometry with you all through my article.
Properties and theorems for geometry:
Property 1: If any two points on a plane, there is one and only one line containing them.
Property 2: Two distinct lines cannot have more than one point in common
Property 3: If a line and a point not on it, there is one and only one line that passes through the given point and is parallel to the given line.
Property 4: If the given two lines intersect, then the vertically opposite angles are equal.
Property 5: If a given transversal intersects two parallel lines, then any pair of corresponding angles are equal.
Property 6: If any two sides and the included angle of one triangle are equal to any two sides and the included angle of another triangle, then the two triangles are congruent
Theorem 1:
The given two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle.
Draw a triangle ABC and a line XY parallel to the side BC (see Figure). Mark the point of intersection of line XY and the side AB as D, and the point of intersection of the line XY and the side AC as E. Since the side AB and the side AC are transversal of the parallel line segments XY and BC,
∠D = ∠B, ∠E = ∠C
The two triangles ABC and ADE have AAA property. However, they are not congruent since the corresponding sides are not equal. Hence, we conclude that AAA correspondence cannot be a criterion for congruency of triangles.
Having problem with wb primary keep reading my upcoming posts, i will try to help you.
Example Problems - Geometry:
Example problem 1:
Find the supplement of the following angles:
(i) 70° (ii) 45° (iii) 120° (iv) 155°
Solution:
Since the sum of supplementary angles is 180°,
(i) the supplement of 70° is 180° − 70° = 110°.
(ii) the supplement of 45° is 180° − 45° = 135°.
(iii) the supplement of 120° is 180° − 120° = 60°.
(iv) the supplement of 155° is 180° − 155° = 25°.
Example problem 2:
If the angles of a triangle are in the ratio 4 : 4 : 7, find them.
Solution:
Let the angles be 4x, 4x, 7x.
Then 4x + 4x + 7x = 180° or 15x = 180° or x = 12°.
The angles are 4 × 12°, 4 × 12°, 7 × 12°, or 48°, 48°, 84°.
This is how problems solved using geometry meaning.
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