About Lesson
Lines That Don’t Meet
Method of construction of a line parallel to a given line, using only a sheet of paper
 Take a piece of paper.
 Fold it in half and unfold the line l. Mark a point A on paper outside l.
 Fold the paper perpendicular to the line such that this perpendicular passes through A. Name the perpendicular AN.
 Make a fold perpendicular to AN through point A. Name the new perpendicular line as m.
 Now, l  m.
Steps of construction of a line parallel to a given line
 Take a line l and a point A outside l.
 Take any point B on l and join it to A.
Let’s Build Triangles
Classification of triangles based on sides and angles
Triangles can be classified based on their:
 SIDES:
 Equilateral triangle: All three sides are equal in measure.
 Isosceles triangle: Two sides have equal measure.
 Scalene triangle: All three sides have different measures.
 ANGLES:
 Acute triangle: All angles measure less than 90^{0}.
 Obtuse triangle: One angle is greater than 90^{0}.
 Right triangle: One angle is 90^{0}.
Important properties of triangles
 The exterior angle is equal to the sum of interior opposite angles.
 The sum of all interior angles is 180°
 Sum of the lengths of any two sides is greater than the length of the third side.
 Pythagoras theorem: In any rightangled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Triangles can be constructed if any of the following measurements are given
 Three sides.
 Two sides and an angle between them.
 Two angles and a side between them.
 The hypotenuse and a leg in case of a rightangled triangle.
Construction of triangles given a criterion are listed below:

Construction of a triangle with SSS criterion.
 Construct a triangle ABC, given that AB = 4.5 cm, BC = 5 cm and AC = 6 cm.
Steps: Make a rough sketch for your reference
 Draw a line segment BC = 5 cm
 Construct a triangle ABC, given that AB = 4.5 cm, BC = 5 cm and AC = 6 cm.
Introduction to Constructions of basic figures
Basic constructions:
– To draw a line segment of given length
– a line perpendicular to a given line segment
– an angle
– an angle bisector
– a circle
 In geometry, you have already studied basic constructions.
 To recap, some of them are:
 Drawing a line segment of given length
 Drawing a line perpendicular to a given line segment.
 Angles
 Angle bisectors
 Circles
 Tools used for simple constructions are ruler, protractor and a compass.
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