G_Triangle_8_Lesson 3

Line and Angles Overview

Browse the course units below.

Triangle

Introduction

Triangle

sum=180

Triangle

Types

Game 1

Type: Angle

Game 2

Type: Sides

Quiz

Triangle

Triangle

Isosceles Theorem

Mooc Test

Triangle Angle

Test 1

BLE Q9(b)

Test 1

BLE 9(a,c)

Test 2

BLE 9(b)

Mooc

Test

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, हुन्छन्, र त्रिभुजको आन्तरिक कोणहरूको योगफल सधैँ \(180^\circ\) हुन्छ

त्रिभुजको बाह्य कोणहरूको योगफल सधैँ \(360^\circ\) हुन्छ

Experimental Verification

Fig No	∠A	∠B	∠C	Sum
1
2
3

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.

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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.

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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):

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Test your understanding: Q2

Identify the type of triangle (based on sides):

Test your understanding: Q3

Quiz Complete!

Your final score is:

1. given
   Let \(\triangle ABC\) be an isosceles triangle in which \(AC = BC\).
2. to prove
   Angles opposite to the sides \(AC\) and \(BC\) are equal, that is, \(\angle CAB = \angle CBA\).
3. plan
   Draw a midpoint D of \(AB\) and join \(CD\).
4. proof
   

   SN	Statement	Reasons
   1	\(\triangle ACD \cong \triangle BCD\)	by RHS
   2	\(\angle x = \angle y\)	By CACT

Triangle Angle Quiz

If needed, use a figure given below, and answer the questions given below.

In equilateral triangle ABC, what is the measure of angle A?

In isosceles triangle ABC (AB = AC), angle A is ___°. What is the measure of angle B?

In triangle ABC, angle A = ___° and angle B = ___°. What is the measure of angle C?

Quiz Summary

1. In the adjoining figure, find the values of \(x\) and \(y\). [2U]
2. In the adjoining figure, if \(PQ \parallel RS\), then find the measure of \(\angle QRS\). [2U]
3. Write down the two distinct properties between parallelogram and rhombus. [2U]
4. Find the value of \(\angle BAC\) in the given \(\triangle ABC\). [2U]
5. In the adjoining figure, find the values of \(x\) and \(y\). [2U]
6. In the given figure, find the value of \(x\). [2U]
7. Calculate the values of angles \(a\) and \(b\) in the given figure. [2U]
8. In \(\triangle XYZ\), if \(2\angle X = 3\angle Y = 6\angle Z\), find the values of all the angles. [2HA]
9. In equilateral \(\triangle POR\), if one side \(PQ = 6\) cm, find its perimeter and area. [2U]
10. In \(\triangle DEF\), if \(DE = EF = DF = 8\) cm, find its area and also write what are the measurements of its angles. [2U]