Page 113 - classs 6 a_Neat

EXAMPLE 2: Construct an angle of 105° with the help of a protractor. 1. A measure of 90° is called a right angle.
2. A measure of 180° is called a straight angle.
Method Draw a ray OA. Place the protractor in such a way that its centre lies exactly at O and 3. An angle less than 90° is called an acute angle.
the base line lies along OA. Starting from 0° on the side of A, move the eyes and look 4. An angle more than 90° and less than 180° is called an obtuse angle.
for the 105° mark on the protractor. Mark a point B against this 105° mark. 5. An angle more than 180° and less than 360° is called a reflex angle.
Remove the protractor and draw the ray OB. 6. An angle whose degree measure is 360° is called a complete angle.
Then, AOB is the required angle whose measure is 105°. 7. An angle whose measure is 0° is called a zero angle.

TRIANGLE

Triangle Let A, B and C be three noncollinear points.

Then, the figure formed by the three line segments AB,BC
and CA is called a triangle with vertices A,B and C.
Such a triangle is denoted by the symbol .∆ABC.

PERPENDICULAR LINES
A. ∆ABC has:

PERPENDICULAR LINES Two lines land mare said to be perpendicular to each other if one of the angles (i) three sides, namely, AB, BC and CA;
formed by them ts a right angle, and we write l- m (read as I is perpendicular tom). (ii) three angles, namely, BAC, ABC and BCA to be denoted by A, B and C respectively.

Two rays are said to be perpendicular to each other if the The three sides and three angles of a triangle are together called the six parts or six elements of the triangle.
corresponding lines determined by them are perpendicular
to each other. In .∆ABC, the points A, Band Care called its vertices.
Clearly, A is the vertex opposite to the side BC.
Two segments are said to be perpendicular to each other if the Similarly, Bis the vertex opposite to the side CA.
corresponding lines determined by them are perpendicular And, C is the vertex opposite to the side AB.
to each other.
CONGRUENT TRIANGLES Two triangles are said to be
A ray and a segment are said to be perpendicular to each other if congruent if every angle of one is equal to the corresponding angle
the corresponding lines determined by them are perpendicular of the other and every side of one is equal to the corresponding side
to each other. of the other.

Construction of a line perpendicular to a given line
∆ ABC and .∆ DEF are congruent triangles because A = D,
EXAMPLE 3: Draw a line l and mark a point A on it. Construct a line perpendicular to the B= E, C = F, AB = DE, BC = EF and CA = FD.
line l at the point A, using a protractor
Method Let l be the given line and A be the given point on it. INTERIOR AND EXTERIOR OF A TRIANGLE
Place the protractor on l in
such a way that its centre is (1) The part of the plane enclosed by ∆ABC is called the interior oft:∆ ABC.
exactly on the point A and its ∆ ABC is the boundary of its interior.
base line lies along l.
Holding the protractor fixed, (ii) The part of the plane not enclosed by ∆ABC is called the exterior of ∆ABC.
mark with a pencil a point B
on the paper against the 90° And, D lies on ∆ABC.
mark of the protractor.
Remove the protractor and Remark: If p and Q are two interior points of ∆ ABC then the line segment PQ lies entirely in the
with a ruler draw a line interior of ∆ABC.
passing through A and B.
Then, AB l - l at A