- The six elements of a triangle are its three angles and the three sides.
- The line segment joining a vertex of a triangle to the mid point of its opposite side is called a median of the triangle.
- A triangle has 3 medians.
- The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle.
- A triangle has 3 altitudes.
- An exterior angle of a triangle is formed, when a side of a triangle is produced.
- The measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.
- The sum of the three angles of a triangle is 180°.
- A triangle is said to be equilateral, if each of its sides has the same length.
- In an equilateral triangle, each angle has measure 60°.
- A triangle is said to be isosceles if at least two of its sides are of same length.
- The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
- The difference of the lengths of any two sides of a triangle is always smaller than the length of the third side.
- In a right-angled triangle, the side opposite to the right angle is called the hypotenuse and the other two sides are called its legs or arms.
- In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on its legs.
- Two plane figures, say, F1 and F2 are said to be congruent, if the trace-copy of F1 fits exactly on that of F2.
- We write this as F1 ≅ F2.
- Two line segments, say ABand CD , are congruent, if they have equal lengths.
- We write this as AB CD ≅ .
- However, it is common to write it as AB = CD .
- Two angles, say ∠ABC and ∠PQR, are congruent, if their measures are equal.
- We write this as ∠ABC ≅ ∠ PQR or as m ∠ABC = m∠PQR or simply as ∠ ABC = ∠ PQR.
- Under a given correspondence, two triangles are congruent, if the three sides of the one are equal to the three sides of the other (SSS).
- Under a given correspondence, two triangles are congruent if two sides and the angle included between them in one of the triangles are equal to the two sides and the angle included between them of the other triangle (SAS).
- Under a given correspondence, two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle (ASA).
- Under a given correspondence, two right-angled triangles are congruent if the hypotenuse and a leg (side) of one of the triangles are equal to the hypotenuse and one of the leg (side) of the other triangle (RHS)
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