Triangles Questions

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Triangles are considered basic geometrical shapes, which we can see in our everyday lives. Thus, children must learn about different types of triangles. Check out the well-made triangle questions and answers PDF for a better understanding of this topic. 


Classifications of Triangles

Types of Triangle Based on the measure of sides as follows -


I. Isosceles Triangles

The kind of Triangle which has two of its sides equal is called Isosceles Triangle. 

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II. Equilateral Triangle

The kind of triangles which have triangle sides equal is called the Equilateral Triangle. 

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III. Scalene Triangle

The type of Triangle which has all its sides equal is called a scalene triangle. 

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Types of Triangles Based on Angles

  1. Acute-angled Triangle

  2. Obtuse-angled Triangle

  3. Right-angled Triangle 


Acute Triangle

An acute triangle is a Triangle where all Triangle interior angles are acute, which is less than 90 degrees. The figure given below shows an acute-angled triangle.


Obtuse Triangle

Obtuse Triangle is a Triangle in which all three interior angles are an obtuse angle; that is, it is greater than 90 degrees. The figure given below illustrates an obtuse triangle.


Right Triangle

A right triangle is a type of Triangle that has one of its angles as 90 degrees. In a right-angled triangle, 

Hypotenuse - The longest side opposite to the right angle (90-degree angle) 


The Perimeter of the Triangle

The sum of all three of the sides is called the Perimeter of a triangle.


Area of a Triangle from Sides

There are two ways to calculate the Area of the Triangle


1. Area=(1Trianglese x Height)

The area of a triangle is quite interesting. Often it will be represented by Area=(1/2) x Base x Height. Where the height has calculated an altitude drawn from the base to the opposite angle. This formula makes for a relatively easy calculation of a triangle area. Still, it isn't easy to naturally find a triangle given in terms of at least one side (the base) and a height. 


2. Hero Formula 

This formula is attributed to Heron of Alexandria. The Hero formula is given by 

Area=SQRT(s(s-a)(s-b)(s-c)),

where s=(a+b+c)/2 or perimeter/2.


Congruent Triangles

A Triangle is a polygon having three line segments forming three angles is known as Triangle.

Two Triangles are considered to be congruent if their corresponding sides have the same length and angles have the same measure. Thus two triangles can easily be superimposed side to side and angle to angle.


Similarity Criteria of Triangles

There are few criteria to find whether the given two triangles are similar or not:

  • Side-Side- Side (SSS) Similarity Criterion – 

According to these criteria, the corresponding sides of any two triangles are in the same ratio. Their corresponding angles will be equal in measure, and the Triangle will be congruent as similar triangles.

  • Angle Angle Angle (AAA) Similarity Criterion 

 According to these criteria, triangles are considered similar when the corresponding angles of any two triangles are equal; then, their corresponding side will be in the same ratio. 

  • Angle-Angle (AA) Similarity Criterion 

According to these criteria, triangles are considered similar  When two angles of one Triangle are respecTrianglequal to the two angles of the other Triangle.

  • Side-Angle- Side (SAS) Similarity Criterion 

According to these criteria, triangles are considered similar When one angle of a triangle is equal to another triangle angle. And also, the sides, including these angles, are in the same ratio (proportional). 

Go through some samples based on heron's formula questions, area of triangle questions; triangles class 10 important questions congruent triangles questions, similar triangles multiple choice questions with answers and congruent triangles exam which will help you understand the concept very well and prepare well for your exam. 

FAQ (Frequently Asked Questions)

1. If A ABC ~ ARPQ, AB = 3 cm, BC = 5 cm, AC = 6 cm, RP = 6 cm and PQ = 10 cm, then Find QR.

Solution:  ΔABC ~ ΔRPQ

So, AB/RP = BC/PQ = AC/RQ  as similar triangles have proportional sides

3/6=5/10=6/QR

½ = ½ 6/QR

QR= 12 cm 

2. Find the Area of a Triangle Whose Two Sides are 12 cm and 16 cm and the Perimeter is 42cm.

Ans. Assume that the third side of the triangle to be “x”.

Now, the three sides of the triangle are 12 cm, 16 cm, and “x” cm

It is given that the perimeter of the triangle = 36cm

So, x = 36 – (12 + 16) cm = 8 cm

∴ The semi perimeter of triangle = 36/2 = 18

Using Heron’s formula,

Area of the triangle,

= √[s (s-a) (s-b) (s-c)]

= √[18(18 – 12) (18 – 16) (18 – 8)] cm²

= √[18 × 6 × 2 × 11] m²

= 18√132 cm²

3. Corresponding Sides of Two Similar Triangles are in the Ratio of 1:2. If the Area of Small Triangle is 16 sq. cm, then the Area of Large Triangle is:

(a) 30 sq.cm.

(b) 6 sq.cm

(c) 7 sq.cm.

(d) 4 sq.cm

Answer: d

Solution: Let A1 and A2 are areas of the small and large triangle.

Then,

A2/A1=(side of large triangle/side of the small triangle)

A2/18=(1/2)2

A2=108 sq.cm.

4. Sides of Two Similar Triangles are in the Ratio 1: 9. Areas of these Triangles are in the Ratio

(a)2: 81

(b)1: 9

(c)1: 16

(d)16: 81

Answer: c

Explanation: Let ABC and DEF are two similar triangles, such that,

ΔABC ~ ΔDEF

And AB/DE = AC/DF = BC/EF = 1/9

As the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides,

∴ Area(ΔABC)/Area(ΔDEF) = AB2/DE2

∴ Area(ΔABC)/Area(ΔDEF) = (1/9)2 = 1/81 = 1: 81