Mathematics-form 3-chapter 1 Lines And Angle Ii By Kelvin 4a351a

Mathematics Form 3 – Chapter 1

Notes Prepared by Kelvin

Form 3 - Chapter 1 - Lines and Angle II [Notes Completely] Review Form 1 - Chapter 9 - Lines and Angle

9.1 Angles To compare and classify angles Name of angle

Value of angle

Acute angle

0° < 90°

Right angle

=90°

Obtuse angle

90° < 180°

Straight angle

= 180°

Reflex angle

180° < 360°

Whole angle

=360°

Diagram of angle

Table 1

Determine the angle on a straight line equals 180°. 1. The sum of angles on a straight line is 180˚. 2. In diagram 2, a + b + c = 180°. 3. The value of any angle on a straight line can be found by subtracting the angle given from 180°. Determine the angle on a complete turn equals 360°. 1. The sum of angles on a straight line is 360˚. 2. In diagram 3, a + b + c = 360°. 3. The value of any angle on a whole turn can be found by subtracting the angle given from 360°. 9.2 Parallel and perpendicular lines To determine parallel lines Parallel lines are: a) two straight lines do not intersect or meet a point. b) distance between the lines are always the same.

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Mathematics Form 3 – Chapter 1

Notes Prepared by Kelvin

In diagram 4, shown arrows are parallel. AB is parallel to CD (AB//CD) PQ is parallel to RS (PQ//RS) To determine perpendicular lines In diagram 5, shown a perpendicular line. Perpendicular lines are two straight lines intersect at a right angle. AB is perpendicular to CD (AB CD) To state the angle formed by perpendicular line In diagram 6, shown two straight lines are intersecting. Line AB intersects with line CD at point O. The angles formed are ∠ AOC, ∠ BOC, ∠DOB, and ∠ DOA ∠ AOC = 90°, ∠ BOC= 90°, ∠ DOB= 90°, and ∠ DOA= 90°. 9.3 Intersecting lines To identify intersecting lines Intersecting lines are two straight lines meet a point. The point is called point of intersection. In diagram 7, AB intersects CD at point O. 9.4 Vertically opposite, adjacent, complementary and supplementary angles To determine properties of vertically opposite angles Vertically opposite angles are formed by two intersecting lines. a and c are vertically opposite angles (a=c) b and d are vertically opposite angles (b=d) To determine properties of adjacent angles In diagram 9, shown an adjacent angle. Adjacent angles are two angles which is side by side with a common vertex and a common side. In the following diagram, ∠ABC and ∠CBD are side by side. Point B is the common vertex. BC is the common side. To determine properties of complementary angles In diagram 10, shown a complementary angle. Complementary angles are two angles whose sum is 90°. a+b=90°. To determine properties of supplementary angles In diagram 10, shown a supplementary angle. Supplementary angles are two angles whose sum is 180°. a+b=180°.

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Mathematics Form 3 – Chapter 1

Notes Prepared by Kelvin

Form 3 – Chapter 1 - Lines and Angle II In this chapter, you will learn: 1- Transversal is …………………….……………………………………………… Transversal crossing Transversal crosses Transversal cuts across two lines two parallel lines three lines

2- Parallel line is ……………………………………………………………………

3- Corresponding Angles, Interior Angles and Alternate Angles These lines are parallel, These lines are not parallel, These lines are parallel, because a pair of because a pair of Interior because a pair of Corresponding Angles Angles do not add up to 180°. Alternate Angles are are equal. (81° + 101° =182°) equal.

4- To solve problems involving triangles The sum of the angles of a triangle is 180°. This is an example of following example 1. 5- To solve problems involving quadrilaterals The sum of the angles of a quadrilateral is 360°. This is an example of following example 2.

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Mathematics Form 3 – Chapter 1

Notes Prepared by Kelvin

Short Summary:

Exercise 1: AB and CD are parallel lines and EH is a transversal. The size of angle EFB is (2x - 100)° and the size of angle CGF is (x + 52)° What is the actual size of the Angle EFB ? A 12° B 52° C 72° D 128° Exercise 2:

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Mathematics Form 3 – Chapter 1

Notes Prepared by Kelvin

PQ and RS are parallel lines and TW is a transversal. The size of angle TUQ is (x + 12)° and the size of angle SVW is (3x + 48)° What is the value of x? A x = 18 B x = 20 C x = 30 D x = 42

Activity 1:

Activity 2:

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Mathematics Form 3 – Chapter 1

Notes Prepared by Kelvin

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