Learning objectives
● To understand about adjacent angles, linear pair and vertically opposite angles.
● To understand transversal.
● To identify the different types of angles formed by a pair of lines wilth a transversal.
● To construct perpendicular bisector of a given line segment.
● To construct angle bisector of a given angle.
● To construct special angles such as 90°, 60°, 30° and 120° without using protractor.

__Chapter 5__

__GEOMETRY__

** **

**Learning objectives**

● To understand about adjacent angles, linear pair and vertically
opposite angles.

● To understand transversal.

● To identify the different types of angles formed by a pair of lines
wilth a transversal.

● To construct perpendicular bisector of a given line segment.

● To construct angle bisector of a given angle.

● To construct special angles such as 90°, 60°, 30° and 120° without
using protractor.

__Recap__

**Lines**

Let us recall the following concepts on lines and
points which we have learnt in class VI.

A **line**
extends along both directions without any end. A line AB is denoted by . Sometimes small letters like *l*, *m*, *n* and so on are used to denote lines.

**A line segment **has two end points. The line segment
'AB' is represented by .

A **Ray**
is a line that starts from a point 'A' and extends without any end in a particular
direction passing through 'B' which is denoted by .

If two lines *m* and *n* are parallel, then we denote it as *m||n*. **Parallel lines** never intersect each other.

When two lines have a common point they are called
**intersecting lines** and that point is called
the point of intersection of the given two lines.

If three or more points lie on the same line, then
they are called **collinear points**; otherwise
they are called **non-collinear points**.

**Try these**

1. Complete the following statements.

(i) A ** line** is a straight path that goes on endlessly in two directions.

(ii) A ** line segment** is a line with two end points.

(iii) A ** ray** is a straight path that begins at a point and goes on
and extends endlessly in the other direction.

(iv) The lines which intersect at right angles are ** perpendicular lines**.

(v) The lines which intersect each other at a point are called ** Intersecting lines**.

(vi) The lines that never intersect are called ** parallel lines**.

2. Use a ruler or straightedge to draw each figure.

(i) line *CD* (ii) ray *AB* (iii) line segment *MN*

3. Look at the figure and answer the following questions.

(i) Which line is parallel to *AB* : **GH**

(ii) Name a line which intersect
*CD : ***IJ*** *

(iii) Name the lines which are perpendicular to *GH ***: KL**

(iv) How many lines are parallel
to *IJ*

**one line KL**

(v) Will EF intersect *AB*? Explain.

**NO EF intersect KL**

**Angles**

Recall that **an angle**
is formed when two rays diverge from a common point. The rays forming an angle are
called the **arms** of the angle and the common
point is called the **vertex **of the angle. You have studied different types of angles, such
as** acute angle, right angle, obtuse angle,
straight angle **and** reflex angle, **in class
VI. We can** **summarize them as follows:

**Acute angle**

An angle whose measure is less than 90º is called
an acute angle.

**Right angle**

An angle whose measure is exactly 90º is called
a right angle.

**Obtuse angle**

An angle whose measure is greater than 90º is called
an obtuse angle.

**Straight angle**

An angle whose measure is exactly 180° is called
a straight angle.

**Reflex angle**

An angle whose measure is greater than 180° and
less than 360° is called a reflex angle.

Also, we have studied about related angles such
as complementary and supplementary angles in our previous class. Let us recall them.

**Complementary angles**

Two angles are called Complementary
angles if their sum is 90°.

Are the two angles given in the figure complementary?
Yes.

The pair of angles 35° and 55° are complementary, where the angle 35° is said to be the complement of the other angle 55° and vice versa.

**Supplementary angles**

Two angles are called Supplementary
angles if their sum is 180°.

Observe the sum of measures of the angles 70° and
110° given in the figure is 180°. When two angles are supplementary, each angle
is said to be the supplement of the other.

** **

**Try these**

**Choose the correct answer.**

**1. A straight angle measures**

(a) 45°

(b) 90°

(c) 180°

(d) 100°

*Answer :***(c) 180°**

**2. An angle with measure 128° is called
____________ angle.**

(a) a straight

(b) an obtuse

(c) an acute

(d) Right

*Answer :***(b) an obtuse**

**3. The corner of the A4 paper has**

(a) an acute
angle

(b) a right
angle

(c) straight

(d) an obtuse
angle

*Answer :***(b) a right
angle**

**4. If a perpendicular line is bisecting
the given line, you would have two**

(a) right
angles

(b) obtuse
angles

(c) acute
angles

(d) reflex
angles

*Answer :***(a) right
angles**

**5. An angle that measure 0° is called
_______.**

(a) right
angle

(b) obtuse
angle

(c) acute
angle

(d) zero
angle

*Answer :***(d) zero angle**

**Introduction**

We are familiar with complementary and supplementary
angles. Let us see some more related pairs of angles now.

**MATHEMATICS ALIVE - GEOMETRY IN REAL LIFE **

**Beauty
of Angles in architecture and kolams**

Tags : Term 1 Chapter 5 | 7th Maths , 7th Maths : Term 1 Unit 5 : Geometry

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