Students can go through AP 7th Class Maths Notes Chapter 5 Lines and Angles to understand and remember the concepts easily.
Class 7 Maths Chapter 5 Notes Lines and Angles
→ Point: A dot on a paper gives the idea of a point
→ Line : Set of points extending in both directions in a straight path results a line.
Ex : 
→ Line AB is denoted by \(\overrightarrow{\mathrm{AB}}\).
→ We use letters like, l, m, n, etc for denoting lines.
→ Line segment: A part of line is called line segment.
Ex : 
→ Line segment PQ is denoted by \(\overline{\mathrm{PQ}}\).
→ Number of points on a line is infinite.
→ A ray has only one end point.
→ Set of points extending only in one direction is called a Ray.
Ex : \(\overrightarrow{\mathrm{OA}}\), \(\overrightarrow{\mathrm{OB}}\) are two rays.
→ Angle : The union of two rays having same initial. point is called an angle
Ex : ∠AOB is an angle.
→ Types of angles
1) Acute angle: An angle whose measure is less than 90° is called an Acute angle.
Ex: 1) 70°, 35°, 80°, 45°, etc.
2) Obtuse angle : An angle whose mea¬sure is greater than 90° but lesfc than 180° is called obtuse angle.
Ex: 1) 110°, 120°, 130°, ……..
3) Right angle : An angle whose measure is 90° is called a Right angle.
Ex: 1) 90° means Right angle
4) Reflex angle: An angle whose measure is more than 180° and less than 360° is called Reflex angle
Ex: 1) 186° 2) 211°
5) Straight angle : An angle whose measure is 180° is called a straight angle.
Ex : 1) 180°(or) 2 right angles
6) Complete angle : An angle whose mea-sure is equal to 360° is called a comp¬lete angle.
Ex : 1) 360°(or) 4 right angles
→ Complementary Angles: If the sum of two angles is 90° (or) Right angle then those two angles are called complementary angles.
Ex : 1) 60° and 30°
2) 45° and 45°
3) 50° and 40°
→ Complementary angles are always acute.
→ Supplementary angles : If the sum of two angles is 180° then they are called as supplementary angles.
Ex : 1) 120,60°
2) 80°, 100°
3) 110°, 70°
→ If two angles are supplementary and one of the angles is obtuse then other angle is acute.
Ex : 1) The supplementary angle of 120° is 180°- 120° = 60°
2) The supplementary angle of 100° is 180° – 100° = 80°
→ If two angles are supplementary and one of the angles is acute then other angle is obtuse.
Ex : 1) The supplementary angle of 50° is 180°- 50°= 130°
2) The supplementary angle of 75° is 180° – 75° = 105°
→ Adjacent Angles : The angles that are such that
- they have common vertex.
- they have a common arm.
- the non-common arms are on either side of the common arm.
Such pair’s of angles are called adjacent.
→ Linear Pair : A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.
Ex : 
→ Linear Angles : If two or more angles are adjacent to each other, then they are linear angles.
Ex : 
→ If two angles are equal and form a linear pair then each is equal to 90°.
Ex : 
a + b = 180°
a = b = 90°
→ Vertically opposite angles : Observe the following figure,
∠a is vertically opposite to ∠c.
∠b is vertically opposite to ∠d.
∴ ∠a = ∠c ; ∠b = ∠d
∠a + ∠b = 180°; ∠b + ∠c = 180°
∠c + ∠d = 180°; ∠a + ∠d = 180°
→ If two lines intersect, the vertically opposite angles so formed are equal.
∠1 = ∠3
∠2 = ∠4
→ Intersecting lines : Two lines l and m intersect if they have a point in common. This common point ‘O’ is their point of intersection.
→ Transversal: A line that intersects two or more lines at distinct points is called a transversal.
→ Angles made by a Transversal
Interior angles ∠3, ∠4, ∠5, ∠6
Exterior angles ∠1, ∠2, ∠7, ∠8
Pairs of Corresponding angles ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8
Pairs of Alternate inferior angles ∠3 and ∠6, ∠4 and ∠5
Pairs of Alternate exterior angles ∠1 and ∠8, ∠2 and ∠7
Pairs of inferior angles on the same side of the transversal ∠3 and ∠5, ∠4 and ∠6
→ Different position of corresponding angles
→ Alternate interior angles
i) have different vertices
ii) are on opposite sides of the transversal and
iii) lie ‘between’ the two lines
→ Transversal of Parallel Lines :
- If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
∠7 = ∠8 ; ∠5 = ∠6
∠1 = ∠2 ; ∠3 = ∠4 - If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal.
∠1 = ∠6 ; ∠3 = ∠8 - If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary.
∠1 + ∠8 = 180°; ∠3 + ∠6 = 180° - From the above figure we can write the following properties also
- ∠5 = ∠2 (Alternate exterior angles) ∠7 = ∠4
- ∠7 + ∠2 = 180° (Sum of exterior ∠5 + ∠4 = 180° angles on the same side of transversal is 180°)
→ When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.
→ When a transversal cuts two lines such that pair of alternate interior angles are equal, then the lines have to be parallel.
→ When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary the lines have to be parallel.