$altitude geometry special rule$

#ALTITUDE GEOMETRY SPECIAL RULE SERIES#

The necessary and sufficient conditions for two triangles to be similar are as follows: It is written as в€† ABC в€ј в€† XYZ and said as в€† ABC вЂis similar toвЂ™ в€† XYZ. Two triangles are said to be similar if the corresponding angles of two triangles are congruent and lengths of corresponding sides are proportional. They remain similar even if they are moved or rotated. Two geometrical shapes are congruent if they cover each other exactly.ДЇigures with same shape but with proportional sizes are similar figures. The shapes would also remain congruent if we reflect the shapes by producing mirror images. If two shapes are congruent, they remain congruent even if they are moved or rotated. Here, в€ ACD is the exterior angle to the в€†ABC.ДЄccording to the exterior angle property, в€ ACD = в€ CAB + в€ ABC.ДЇigures with same size and shape are congruent figures. This is called the exterior angle property of a triangle. An exterior angle of a triangle is equal to the sum of its interior opposite angles.In the figure above, в€ A is the largest angle and the side opposite to it, BC is the largest side of the triangle. In the figure above, в€ B is the largest angle and the side opposite to it (hypotenuse), is the largest side of the triangle. The side opposite to the largest angle is the longest side of the triangle and the side opposite to the smallest angle is the shortest side of the triangle.Similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.The sum of the angles in a triangle is 180В°.Like any other right triangle, these two triangles satisfy the Pythagorean Theorem. The sides in a 30-60-90 triangle are in the ratio 1 : в€љ3 : 2 This is a scalene right triangle as none of the sides or angles are equal. The sides in a 45-45-90 triangle are in the ratio 1 : 1 : в€љ2.ДЄ 30-60-90 triangle, as the name indicates, is a right triangle in which the other two angles are 30В° and 60В°. As of now, our focus is only on a special pair of right triangles.ДЄ 45-45-90 triangle, as the name indicates, is a right triangle in which the other two angles are 45В° each. There are different types of right triangles. Hence, the Pythagorean Theorem helps to find whether a triangle is Right-angled. Only a triangle that satisfies this condition is a right triangle. In the figure above, the side opposite to the right angle, BC is called the hypotenuse. Right-angled triangle: A triangle whose one angle is a right-angle is a Right-angled triangle or Right triangle. Obtuse-angled triangle: A triangle whose one angle is obtuse is an obtuse-angled triangle or Obtuse triangle. Scalene triangle: A triangle having three sides of different lengths is called a scalene triangle.ДЄcute-angled triangle: A triangle whose all angles are acute is called an acute-angled triangle or Acute triangle. The two angles opposite to the equal sides are equal. Isosceles triangle: A triangle having two sides of equal length is an Isosceles triangle. Since all sides are equal, all angles are equal too.

There are three types of triangles based on sides and three based on angles.Д®quilateral triangle: A triangle having all the three sides of equal length is an equilateral triangle. In the figure above, AB, BC, CA are the three line segments and в€ A, в€ B, в€ C are the three angles.

#ALTITUDE GEOMETRY SPECIAL RULE SERIES#

In the series on the basic building blocks of geometry, after a overview of lines, rays and segments, this time we cover the types and properties of triangles.Дefinition: A triangle is a closed figure made up of three line segments.ДЄ triangle consists of three line segments and three angles.

Altitude geometry special rule