TRIANGLE

• The points A, B and C called the vertices (vertex) of the triangle
• The line AB, BC and AC are called the sides of the triangle
• ∠ABC, ∠BAC and ∠BCA are called the interior angles of the triangle
• The symbol of triangle ΔABC

There are 6 types of triangle which are:

• Equilateral triangle (all the sides have the same length)
• Isosceles triangle (two sides are equal in length)
• Scalene triangle (no sides are equal in length)
• Acute-angled triangle (all the angles are less than 90º
• Right-angled triangle (one of the angle is 90º)
• Obtuse-angles triangle (one of the angle is greater than 90º)

To construct triangle, we must know either one of the following sets of quantitie:

• Three sides
• Two angles and one side
• Two sides and one angle

UNIT 3: BASIC GEOMETRY – CHAPTER 10: REASONING IN GEOMETRY

Chapter contents

10:01  Adjacent angles

10:02  Angles at a point and vertically opposite angles

10:03  Angles associated with parallel lines

10:05  Angles sum of a quadrilateral

Learning outcomes

Students will be able to:

• Identify and name angles formed by the intersection of straight lines, including those related to transversals on sets of parallel lines, and make use of the relationships between them.
• Classify, construct, and determine the properties of triangles and quadrilaterals.

Explanation

Mathematical terminologies

• Acute: less than 90º
• Obtuse: more than 90º but less than 180º
• Right: 90º
• Complementary: two angles when their sum is 90º
• Supplementary: two anges when their sum is 180º
• Vertically opposite angles: two straight lines intersect each other

Adjacent angles

Adjacent angles is when two or more angles form 90º or 180º.

When the angles form 90º, it is called complementary angle. When the angles form 180º, it is called supplementary angle.

Let’s do some exercises

1. Write down the value of the pronumeral in each of the following.

a.

  x= 20º+15º

x= 35º

b.

 p= 60º+65º

p= 125º

Angles at a point and vertically opposite angles

Angles at a point is usually when 4 angles in the middle form 360º but the angles are not all the same. Vertically opposite angles is when two straight lines cross, two pairs of vertically opposite angles are formed. Vertically opposite angles are equal.

Let’s do some exercises

1. Find the value of the pronumeral in each of the following.

a.

 xº= 360º-140º-120º

xº= 100º

b.

aº= 130º

Angles associated with parallel lines

 When two lines are cut by a third line (called a transversal),                                                   the eight angles shown in Figure 1 are formed. From what we                                                 have learned about vertically opposite angles, we can see that:

angle 1=angle 3     angle 2=angle 4     angle 5=angle 7

angle 6=angle 8

Types of angles:

Let’s do some exercises

1. Find the values of the pronumerals in each of the following, giving a reason for each answer.

a.

 aº= 38º corresponding angles

b.

fº= 85º corresponding angles

 

Angles sum of a quadrilateral

The sum of angles in a quadrilateral is always 360º

Let’s do some excercises

1. Find the value of the pronumeral in each of the following.

a.

 aº= 360º-110º-145º-55º

aº= 50º

b.

 2xº= 360º-105º-78º-67º

2xº= 110º

xº= 55º

 

So that’s all that I can tell you about Chapter 10: reasoning in geometry. Thank you for reading.

References: Mcseveny, A., Conway, R., Wilkes, S., & Smith, M. (2007). International Mathematics 2 for the Middle Years. In A. Mcseveny, R. Conway, S. Wilkes, & M. Smith, International Mathematics 2 for the Middle Years (pp. 250-270). Pearson Australia

GEOMETRY

Mathematical terminologies

• Point:
  • The basic element of geometric figure
  • All other geometrical figure are made up of a collection of points
  • Normally use capital letter (A, B, …)
• Line:
  • Collection of points going on and on infinitely in both directions. No endpoints.
  • Vertically, diagonally and horizontally
  • Has arrows on the end
  • Named by a single lower case letter (a, b, …)
• Line segment:
  • Part of line. It has two endpoints and include all the points between those endpoint.
  • Vertically, diagonally and horizontally
  • Points at the end
  • Named bu the capital letter end point
• Ray:
  • Part of line. Has one endpoint and continues on and on in one directions
  • Vertically, diagonally and horizontally
  • A point at one and and an arrow at the other
  • Named by saying the end point first and then say the name of one other point on the ray
• Collinear point: Points which lie in a straight line
• Concurrent line: Three or more line all passing through a common point
• Perpendicular line: Special intersecting line that form right angle where they intersect
• Parallel line:  Lines which extend in the same direction and remain the same distance apart
• Angle: When two lines meet together
• Cartesian plane:
  • Plane for draw coordinate
  • Horizontal: x-axis
  • Vertical: y-axis
  • Point of intersection of the axis: 0
• x-axis: abscissa
• y-axis: ordinate

UNIT 3: BASIC GEOMETRY – CHAPTER 8: THE NUMBER PLANE

Chapter contents

8:02  Coordinates and the number plane

Learning outcomes

Students will be able to graph and interpret linear relationships on the number plane.

Explanation

Coordinates and the number plane

Cartesian plane or number plane is a plane to draw coordinates. The horizontal line is called as X-axis and the vertical line is y-axis. The point of intersection is 0.

 

Let’s do some exercises

1. Plot the points given.

(3, 7) (-1,1) (-5. 7) (3, 9)

2. Plot the points given and join them in the order given:

(1, -1) (1, 3) (3, 3) (3, -1)

So that’s all that I can tell you about Chapter 8: the number plane. Thank you for reading.

References: Mcseveny, A., Conway, R., Wilkes, S., & Smith, M. (2007). International Mathematics 2 for the Middle Years. In A. Mcseveny, R. Conway, S. Wilkes, & M. Smith, International Mathematics 2 for the Middle Years (pp. 182-185). Pearson Australia.