define line segment collinear points complementary angles linear pair alternate interior angles corresponding angles
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Answer:
Here are some basic definitions and properties of lines and angles in geometry. These concepts are tested in many competitive entrance exams like GMAT, GRE, CAT.
Line segment: A line segment has two end points with a definite length.
line segment
Ray: A ray has one end point and infinitely extends in one direction.
ray
Straight line: A straight line has neither starting nor end point and is of infinite length.
line segment
Acute angle: The angle that is between 0° and 90° is an acute angle, ∠A in the figure below.
acute angle
Obtuse angle: The angle that is between 90° and 180° is an obtuse angle, ∠B as shown below.
obtuse angle
Right angle: The angle that is 90° is a Right angle, ∠C as shown below.
right angle
Straight angle: The angle that is 180° is a straight angle, ∠AOB in the figure below.
Supplementary angles:
supplementary angles
In the figure above, ∠AOC + ∠COB = ∠AOB = 180°
If the sum of two angles is 180° then the angles are called supplementary angles.
Two right angles always supplement each other.
The pair of adjacent angles whose sum is a straight angle is called a linear pair.
Complementary angles:
complementary angles
∠COA + ∠AOB = 90°
If the sum of two angles is 90° then the two angles are called complementary angles.
Adjacent angles:
The angles that have a common arm and a common vertex are called adjacent angles.
In the figure above, ∠BOA and ∠AOC are adjacent angles. Their common arm is OA and common vertex is ‘O’.
Vertically opposite angles:
When two lines intersect, the angles formed opposite to each other at the point of intersection (vertex) are called vertically opposite angles.
opposite angles
In the figure above,
x and y are two intersecting lines.
∠A and ∠C make one pair of vertically opposite angles and
∠B and ∠D make another pair of vertically opposite angles.
Perpendicular lines: When there is a right angle between two lines, the lines are said to be perpendicular to each other.
perpendicular lines
Here, the lines OA and OB are said to be perpendicular to each other.
Parallel lines:
parallel lines
Here, A and B are two parallel lines, intersected by a line p.
The line p is called a transversal, that which intersects two or more lines (not necessarily parallel lines) at distinct points.
As seen in the figure above, when a transversal intersects two lines, 8 angles are formed.
Let us consider the details in a tabular form for easy reference.
Types of Angles Angles
Interior Angles ∠3, ∠4, ∠5, ∠6
Exterior Angles ∠1, ∠2, ∠7, ∠8
Vertically opposite Angles (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)
Corresponding Angles (∠1, ∠5), (∠2, ∠6), (∠3, ∠7), (∠4, ∠8)
Interior Alternate Angles (∠3, ∠5), (∠4, ∠6)
Exterior Alternate Angles (∠1, ∠7), (∠2, ∠8)
Interior Angles on the same side of transversal (∠3, ∠6), (∠4, ∠5)
When a transversal intersects two parallel lines,
The corresponding angles are equal.
The vertically opposite angles are equal.
The alternate interior angles are equal.
The alternate exterior angles are equal.
The pair of interior angles on the same side of the transversal is supplementary.
We can say that the lines are parallel if we can verify at least one of the aforementioned conditions.
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Answer:
1)Line segment: A line segment is a line which has two end points or which has a definite length.
2)Collinear points: When two or more points lie on the same line are called collinear points.
3)Complementary angles: Two pairs of angles whose sum make upto 90 degree is called complementary angle.
4)Linear pairs:Angles which lie on the same line and whose sum add upto 180 degree are called linear pairs.
5)Alternate interior angles:When a line is transversal on two parallel lines it's interior angles which are on the alternative side of the transversal are called alternate interior angles.
6)Corresponding angles:Corresponding angles are angles which are on the same relative position when a transversal crosses two parallel lines.