TRIANGLES: TRIANGLES By Pervinder Singh
What is triangle?: What is triangle? Triangles are one of the fundamental figures used in Euclidean geometry. There are three elements required to make a triangle. It is a 3-sided plane or two-dimensional figure, in which the sum of the interior angles equals exactly 180 degrees.
Classification of triangles: Classification of triangles Equilateral Triangle :- Equilateral means“equal sides,”and in an equilateral triangle, all three sides are the same length.This means that the angles will also be equal – all 60°-making the triangle equiangular as well. Isosceles Triangle :- Isosceles means “equal legs,” and an isosceles triangle has two sides that are equal in length. This also means that the two angles formed where the equal sides meet the third side are equal. Scalene Triangle :- Scalene comes from a word meaning "uneven," and a scalene triangle has three unequal sides. As you might suspect, then, the three angles are unequal as well.
The other triangle classification schema approaches triangles from the point of view of the measurements of the internal angles. It, too, designates three types of triangle. : The other triangle classification schema approaches triangles from the point of view of the measurements of the internal angles. It, too, designates three types of triangle. Acute Triangle . In an acute triangle, the largest internal angle is acute–less than90°.This means that all the angles are acute . Right Triangle . In a right triangle, there is one right angle – an angle of exactly 90°.This means that the other two angles will be acute. Obtuse Triangle . In an obtuse triangle, one internal angle is obtuse. This means, again, that the other two angles will be acute.
Corresponding parts of congruent triangles: Corresponding parts of congruent triangles Triangles that are the same size and shape are congruent triangles . Each triangle has three angles and three sides. If all six corresponding parts are congruent, then the triangles are congruent.
Corresponding parts of congruent triangles: Corresponding parts of congruent triangles A C B X Z Y If Δ ABC is congruent to Δ XYZ , then vertices of the two triangles correspond in the same order as the letter naming the triangles . Δ ABC = Δ XYZ ~
Properties of Triangle Congruence: Properties of Triangle Congruence Congruence of triangles is reflexive , symmetric, and transitive. REFLEXIVE K J L K J L Δ JKL = Δ JKL ~
Slide 8: Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric , and transitive. SYMMETRIC If Δ JKL = Δ PQR, then Δ PQR = Δ JKL K J L Q P R
Slide 9: Properties of Triangle congruency Congruence of triangles is reflexive, symmetric, and transitive . TRANSITIVE K J L Q P R If Δ JKL = Δ PQR, and Δ PQR = Δ XYZ, then Δ JKL = Δ XYZ. Y X Z ~ ~ ~
How to identify congruency of triangle: How to identify congruency of triangle Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size. If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as