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Textbook Solutions Triangles and their Properties - Maharashtra Board

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Chapter 15: Triangles and Their Properties 
 
 
PRACTICE SET 36 [PAGE 80] 
Practice Set 36 | Q 1.1 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? PQR is ... triangle 
 
SOLUTION 
In ?PQR, ?Q = 90
° 
(a right angle) 
Therefore, ?PQR is a right-angle triangle. 
Practice Set 36 | Q 1.2 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? XYZ is ... triangle 
 
SOLUTION 
In ?XYZ, ?Y = 125
° 
(an obtuse angle) 
Therefore, ?XYZ is an obtuse angle triangle. 
Practice Set 36 | Q 1.3 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? LMN is ... triangle 
Page 2


Chapter 15: Triangles and Their Properties 
 
 
PRACTICE SET 36 [PAGE 80] 
Practice Set 36 | Q 1.1 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? PQR is ... triangle 
 
SOLUTION 
In ?PQR, ?Q = 90
° 
(a right angle) 
Therefore, ?PQR is a right-angle triangle. 
Practice Set 36 | Q 1.2 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? XYZ is ... triangle 
 
SOLUTION 
In ?XYZ, ?Y = 125
° 
(an obtuse angle) 
Therefore, ?XYZ is an obtuse angle triangle. 
Practice Set 36 | Q 1.3 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? LMN is ... triangle 
 
SOLUTION 
In ?LMN, all angles are acute angles. 
Therefore, ?LMN is an acute angle triangle. 
Practice Set 36 | Q 2.1 | Page 80 
Observe the figure below and write the type of the triangle based on its sides. 
 
? ABC is ... triangle 
 
SOLUTION 
In ?ABC, all sides are equal. 
Therefore, ?ABC is an equilateral triangle. 
Practice Set 36 | Q 2.2 | Page 80 
Observe the figure below and write the type of the triangle based on its sides. 
 
? DEF is ... triangle 
 
SOLUTION 
In ?DEF, all sides are different. 
Therefore, ?DEF is a scalene triangle. 
Practice Set 36 | Q 2.3 | Page 80 
Observe the figure below and write the type of the triangle based on its sides. 
 
Page 3


Chapter 15: Triangles and Their Properties 
 
 
PRACTICE SET 36 [PAGE 80] 
Practice Set 36 | Q 1.1 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? PQR is ... triangle 
 
SOLUTION 
In ?PQR, ?Q = 90
° 
(a right angle) 
Therefore, ?PQR is a right-angle triangle. 
Practice Set 36 | Q 1.2 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? XYZ is ... triangle 
 
SOLUTION 
In ?XYZ, ?Y = 125
° 
(an obtuse angle) 
Therefore, ?XYZ is an obtuse angle triangle. 
Practice Set 36 | Q 1.3 | Page 80 
Observe the figure below and write the type of the triangle based on its angles. 
 
? LMN is ... triangle 
 
SOLUTION 
In ?LMN, all angles are acute angles. 
Therefore, ?LMN is an acute angle triangle. 
Practice Set 36 | Q 2.1 | Page 80 
Observe the figure below and write the type of the triangle based on its sides. 
 
? ABC is ... triangle 
 
SOLUTION 
In ?ABC, all sides are equal. 
Therefore, ?ABC is an equilateral triangle. 
Practice Set 36 | Q 2.2 | Page 80 
Observe the figure below and write the type of the triangle based on its sides. 
 
? DEF is ... triangle 
 
SOLUTION 
In ?DEF, all sides are different. 
Therefore, ?DEF is a scalene triangle. 
Practice Set 36 | Q 2.3 | Page 80 
Observe the figure below and write the type of the triangle based on its sides. 
 
? UVW is ... triangle 
 
SOLUTION 
In ?UVQ, two sides are equal. 
Therefore, ?UVW is an isosceles triangle. 
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FAQs on Textbook Solutions: Triangles and their Properties

1. What are the different types of triangles based on their sides?
Ans. Triangles can be classified based on their sides into three types: equilateral, isosceles, and scalene. An equilateral triangle has all three sides of equal length, an isosceles triangle has two sides of equal length, and a scalene triangle has all sides of different lengths.
2. How can the angles of a triangle be classified?
Ans. Angles of a triangle can be classified into three categories: acute, right, and obtuse. An acute triangle has all angles measuring less than 90 degrees. A right triangle has one angle that is exactly 90 degrees. An obtuse triangle has one angle that is greater than 90 degrees.
3. What is the sum of the angles in a triangle?
Ans. The sum of the interior angles in any triangle is always 180 degrees. This property holds true for all types of triangles, regardless of their classification based on sides or angles.
4. How do you find the area of a triangle?
Ans. The area of a triangle can be calculated using the formula: Area = 1/2 x base x height. Here, the base is any side of the triangle, and the height is the perpendicular distance from that base to the opposite vertex.
5. What is the Pythagorean theorem and how does it relate to triangles?
Ans. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is fundamental in determining the lengths of sides in right triangles.
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