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Properties of triagles – Part 1

BÀI VIẾT LIÊN QUAN:

property: Thuộc tính

properties of triangles: Các thuộc tính của tam giác

line segment: Đoạn thẳng.

closed figure: Hình khép kín.

The sum of the angles of a triangle: Tổng các góc của một tam giác.

scalene: Lệch, không cân, không đều cạnh.

scalene triangles: Các tam giác thường.

unequal side: Cạnh không bằng nhau.

hypotenuse: Cạnh huyền.

Pythagorean Theorem: Định lý Pitago

opposite: Đối diện

adjacent: Kề, kề nhau

base: Cạnh đáy

height: Chiều cao

perpendicular: Vuông góc

area: Diện tích

perimeter: Chu vi.

perpendicular side or perpendicular leg: Cạnh góc vuông

respectively: Tương ứng, theo thứ tự.

solution: Giải, lời giải, nghiệm (đối với phương trình).

certain: Cho trước, đã biết, chắc chắn.

Certain sets of integers: Tập hợp các số nguyên cho trước. 

A triangle is a closed figure with three sides, each side being a line segment.
The sum of the angles of a triangle is always 180°.

Scalene triangles are triangles with no two sides equal. Scalene triangles also have no two angles equal.

Properties-of-triagles-Part-1_Scalene triangle

Isosceles triangles have two equal sides and two equal angles formed by the equal sides and the unequal side. See the figure below.

Properties-of-triagles-Part-1_Isosceles-triangle

a = b

A = B

C = 180° – 2(A)

Equilateral triangles have all three sides and all three angles equal. Since the sum of the three angles of a triangle is 180°, each angle of an equilateral triangle is 60°.

Properties-of-triagles-Part-1_Equilateral-triangle

a = b = c

∠A = ∠B = ∠C = 60°

A right triangle has one angle equal to a right angle (90°). The sum of the other two angles of a right triangle is, therefore, 90°. The most important relationship in a right triangle is the Pythagorean Theorem. It states that c2 = a2 + b2, where c, the hypotenuse, is the length of the side opposite the right angle, and a and b are the lengths of the other two sides.

Properties-of-triagles-Part-1_Right-triangle

Example: If the two sides of a right triangle adjacent to the right angle are 3 inches and 4 inches respectively, find the length of the side opposite the right angle.
Solution:

Properties-of-triagles-Part-1_Right-triangle

Use the Pythagorean Theorem, c2 = a2 + b2, where a = 3 and b = 4. Then, c2 = 32 + 42 or c2 = 9 + 16 = 25. Thus c = 5.

Properties-of-triagles-Part-1_Right-triangle-Pythagorean-Theorem-1

Properties-of-triagles-Part-1_Right-triangle-Pythagorean-Theorem-2

———End of properties of triangle part 1———

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