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Transactions in the Homes and Offices | Week 18 Topics1 Quiz
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Expansion and Factorization of Algebraic Expressions | Week 24 Topics1 Quiz
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Algebraic Expansion and Factorization of Algebraic Expression | Week 34 Topics1 Quiz
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Algebraic Fractions I | Week 44 Topics1 Quiz
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Addition and Subtraction of Algebraic Fractions | Week 52 Topics1 Quiz
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Linear Inequalities I | Week 74 Topics1 Quiz
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Linear Inequalities II | Week 82 Topics1 Quiz
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Quadrilaterals | Week 92 Topics1 Quiz
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Angles in a Polygon | Week 104 Topics1 Quiz
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The Cartesian Plane Co-ordinate System I | Week 113 Topics1 Quiz
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The Cartesian Plane Co-ordinate System II | Week 121 Topic1 Quiz
Topic Content:
- Angles between Lines and Triangles
- Angles on a Straight Line
- Complementary Angles
- Supplementary Angles
- Vertically Opposite Angles
- Angles at a Point
- Angles in Parallel Lines
- Angles in Triangles
1. Angles on a Straight Line:
In the diagram above
⇒ \( \scriptsize \hat{AOB} \:+\: \hat{BOC} \: + \: \hat{COD} = 180^o\)
That is, a + b + c = 180°
2. Complementary Angles:
a + b = 90°
Example: a = 40°, b = 50°
3. Supplementary Angles:
x + y = 180°
Example: x = 140°, y = 40°
4. Vertically Opposite Angles:
Intersecting lines are lines that cross each other. Vertically Opposite Angles are the angles opposite each other when two lines cross (intersect).
⇒ \( \scriptsize \hat{AOC} = \hat{DOB} \)
⇒ \( \scriptsize \hat{AOD} = \hat{COD} \)
i.e
a = b (vertically opposite angles)
x = y (vertically opposite angles)
5. Angles at a Point:
a + b + c + d = 360°
6. Angles in Parallel Lines:
(a) Alternate Angles:
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
a = b (alternate angles)
x = y (alternate angles)
(b) Corresponding angles:
When two parallel lines are crossed by another line (called the Transversal), the angles in matching corners are called Corresponding Angles.
a = b (corresponding angles)
c = d (corresponding angles)
x = y (corresponding angles)
p = q (corresponding angles)
(c) Co-interior angles:
When a transversal line crosses two parallel line, the two interior angles that occur on the same side of the transversal are called Co-interior angles.
a + b = 180° (co-interior angles)
c + d = 180° (co-interior angles)
7. Angles in Triangles:
(a) The sum of angles in a triangle is 180°;
(b) The exterior angle of a triangle is equal to the sum of the two opposite interior angles;
Point to Note:
When two sides of a triangle are marked with the same line, it means they are equal, and the corresponding angles are equal.
The figure below is an isosceles triangle. Two sides are marked with the same line and are therefore equal and the base angles are therefore equal.
It means,
AB = AC and
\( \scriptsize x = y \) \( \scriptsize \angle B = \angle C \)When all three sides of a triangle are marked with the same line, then all angles are equal and this is known as an equilateral triangle.
