Chapter 6
406 Words
Chapter 6: Geometry
6.1 Introduction to Geometry
Geometry is the branch of mathematics that deals with shapes, sizes, and properties of space. The basic elements of geometry are points, lines, and angles.
Point: A location with no size or shape.
Line: A straight path extending infinitely in both directions.
Angle: Formed by two rays (sides) with a common endpoint (vertex).
6.2 Types of Angles
Acute Angle: An angle less than 90°.
Right Angle: An angle equal to 90°.
Obtuse Angle: An angle greater than 90° but less than 180°.
Straight Angle: An angle equal to 180°.
6.3 Triangles
A triangle is a polygon with three sides and three angles. There are different types of triangles:
Equilateral Triangle: All sides and angles are equal.
Isosceles Triangle: Two sides and two angles are equal.
Scalene Triangle: All sides and angles are different.
6.4 Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
Where aaa and bbb are the lengths of the two legs, and ccc is the length of the hypotenuse.
Exercises
Exercise 1: Identify the types of angles:
50°
90°
120°
180°
75°
Exercise 2: Identify the types of triangles:
Triangle with sides 3 cm, 3 cm, and 3 cm.
Triangle with sides 5 cm, 5 cm, and 8 cm.
Triangle with sides 6 cm, 8 cm, and 10 cm.
Triangle with sides 4 cm, 5 cm, and 6 cm.
Triangle with sides 7 cm, 7 cm, and 10 cm.
Exercise 3: Apply the Pythagorean Theorem:
In a right triangle, if one leg is 3 cm and the other leg is 4 cm, find the length of the hypotenuse.
In a right triangle, if the hypotenuse is 13 cm and one leg is 5 cm, find the length of the other leg.
In a right triangle, if one leg is 8 cm and the hypotenuse is 10 cm, find the length of the other leg.
In a right triangle, if both legs are 6 cm, find the length of the hypotenuse.
In a right triangle, if the hypotenuse is 17 cm and one leg is 8 cm, find the length of the other leg.
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