Triangle

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Congruence in Geometry

Triangle

त्रिभुज भनेको एक बहुभुज हो जसमा तीनवटा भुजाहरू र तीनवटा शिर्षबिन्दुहरू हुन्छन्। शिर्षबिन्दुहरू \(A,B,C\) भएका त्रिभुजलाई \(\triangle ABC\) ले जनाइन्छ। कुनै पनि तीन वटा non-collinear विन्दुहरूले एउटा त्रिभुज निर्धारण गर्दछ।

Click on the grid three times to get a triangle.

Property 1

त्रिभुजका तीन आन्तरिक कोणहरू हुन्छन्, तीन बाह्य कोणहरू, र यसको आन्तरिक कोणहरूको योगफल सधैँ \(180^\circ\) हुन्छ

Property 2

भुजाको आधारमा त्रिभुजलाई तीन प्रकारमा वर्गीकरण गर्न सकिन्छ।

  1. समबाहु त्रिकोण: तीनवटै भुजाहरु बराबर भएको। \(\triangle ABC\)
    An equilateral triangle is a triangle with all three sides equal in length. In an equilateral triangle, each of the interior angles has a measure of 60 degrees.
  2. समद्विबाहु त्रिकोण: कुनै दुईवटा भुजाहरु बराबर भएको। \(\triangle PQR\)
    An isosceles triangle is a triangle with two of its side lengths equal in length. In an isosceles triangle, the angles at the base of the congruent sides are referred to as the base angles and are of equal measures.
  3. विषमबाहु त्रिकोण: कुनै पनि भुजाहरु बराबर नभएको। \(\triangle XYZ\)
    In a scalene triangle, all the side lengths are of different measures and hence, all the angles are of different measures.

Property 3

कोणका आधारमा पनि त्रिभुजलाई तीन प्रकारमा वर्गीकरण गर्न सकिन्छ।

  1. न्युनकोण त्रिभुज: सबै कोणहरू \(90^\circ\) भन्दा साना हुन्छन्। \(\triangle ABC\)
    An acute triangle is a triangle with all three angles measuring less than 90°. In other words, all the angles of an acute triangle are acute angles.
  2. समकोण त्रिभुज: कुनै एक कोण \(90^\circ\) को हुन्छ। \(\triangle PQR\)
    A right triangle is a triangle in which one angle measures 90° and the other two angles measure less than 90°. In a right angled triangle, the side opposite to the right angle is called the hypotenuse while the other two sides are called legs. The hypotenuse is always the longest side while the other two sides are shorter. The below figure shows a right angled triangle PQR in which angle C measures 90°.
  3. अधिककोण त्रिभुज: कुनै एक कोण \(90^\circ\) भन्दा ठूलो हुन्छ। \(\triangle XYZ\)
    An obtuse triangle is a triangle with one angle measuring more than 90° while the other two angles measure less than 90° each. In other words, an obtuse angled triangle has one obtuse angle and two acute angles. The below figure shows an obtuse angled triangle XYZ.

Property 4

Altogether, there are seven types of triangle. The seventh is right isosceles triangle, which is shown in Table

Triangles Based on Sides
Based on Angles Equilateral Isosceles Scalene
Acute Angled x x x
Right Angled x x
Obtuse angled x x

In general, there are 7 types of triangles when classified by a mixture of its angles and lengths. They are equilateral, right isosceles, obtuse isosceles, scalene, acute scalene, right scalene, and obtuse scalene.

Test your understanding: Q1

Identify the type of triangle (based on angles):

Test your understanding: Q2

Identify the type of triangle (based on sides):

Test your understanding: Q3

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