Question

Observe the figures and write the type of the triangle based on its angles.
ΔPQR is ...... triangle.
ΔXYZ is ...... triangle.
ΔLMN is ...... triangle.

Answer 1

Hey there!

Sheena here!
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So before we come directly to the solution to your question I would like to tell you something about Polygons,Triangles And Quadrilateral in brief.

So, What is a Polygon?

Any closed figure made up of Line segments is termed as a Polygon.

There is no specific line segments here, Any number of line segments more than 2 can make a polygon!

What is a Quadrilateral?

Here, A quadrilateral is also a closed figure having only four sides or made up of four line segments.

Remember: Every Quadrilateral is a Polygon but every polygon is not a Quadrilateral.

What is a Triangle?

Triangle is a type of polygon which is made up of 3 line segments or it has 3 sides.

So Now lets come to your Question.

So here we are told to identify the triangles.

To tell you, Triangle is a type of polygon and Triangles are of different types classified in respective to their measures of sides and angles.

We have Triangles classified on the basis of 

Sides

=> Equilateral Triangle: It is a type of triangle in which all sides measure the same i.e all sides are of equal measure.

=> Isosceles Triangle: It is a type of triangle having only 2 sides of equal length.

=> Scalene Triangle: It is a type of triangle having no sides of equal length.

Now, Triangles classified on the basis of

Angles

=> Right angled Triangle: It is a type of triangle having one angle measure as $90^{o}$

=> Acute Angled Triangle: It is a type of triangle having all angles as acute angles i.e having measure less than $90^{o}$

=> Obtuse Angled Triangle: It is a type of triangle having one angle as obtuse angle i.e Having measure more than $90^{o}$

Now, I guess all the terms are cleared.

Now Answer to your question>>>>

Since we are known by the angles,

△PQR is a right angled Triangle.

Reason: It has the symbol i.e the square which indicates that the angle is right angle.

△XYZ is an Obtuse Angled Triangle

Reason: It has one angle which measures more than the measure of right angle.

△LMN is an Acute Angled Triangle

Reason: It has its all angles below the  measure of right angle.
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Please Note: If sides of triangles are given and we are told to identify the type of triangle then the triangles which are classified on the basis of sides should be used.

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Hope this helps!

Thanks!

Answer 2

i ) From figure ( 1 ),

In ∆PQR ,

<PQR = 90°

Therefore ,

If in a triangle one angle 90° then

it is called right angled triangle.

Therefore ,

∆PQR is a right angled triangle .

ii ) From figure ( 2 ),

In ∆XYZ ,

<XYZ = 125° [ obtuse angle ]

If in a triangle one angle is obtuse

angle then it is called obtuse angled

triangle .

Therefore ,

∆XYZ is a Obtuse angled triangle .

iii ) From figure ( 3 ) ,

In ∆LMN ,

all angles are abtuse angles.

If all angles are abtuse angles in a

triangle then it is called abtuse angled

triangle.

Therefore ,

∆LMN is a abtuse angled triangle.

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