Q1: In a triangle, how many medians can be drawn? (a) One (b) Two (c) Three (d) Four
Solution:
Ans: (c) A triangle has three vertices, so we can draw three medians, one from each vertex to the midpoint of the opposite side.
Q2: What is the sum of all interior angles in any triangle? (a) 90° (b) 180° (c) 270° (d) 360°
Solution:
Ans: (b) The angle sum property of a triangle states that the sum of the interior angles of a triangle is always 180°.
Q3: In a right-angled triangle, what is the side opposite to the right angle called? (a) Base (b) Perpendicular (c) Hypotenuse (d) Median
Solution:
Ans: (c) In a right-angled triangle, the side opposite to the right angle is called the hypotenuse, which is the longest side.
Q4: A triangle with all three sides of equal length is called: (a) Equilateral triangle (b) Isosceles triangle (c) Scalene triangle (d) Right-angled triangle
Solution:
Ans: (a) An equilateral triangle has all three sides of equal length and all three angles are equal, each measuring 60°.
Q5: What is the relation between an exterior angle and its interior opposite angles in a triangle? (a) The exterior angle is half the sum of interior opposite angles (b) The exterior angle equals one interior opposite angle (c) The exterior angle is double the sum of interior opposite angles (d) The exterior angle equals the sum of interior opposite angles
Solution:
Ans: (d) According to the exterior angle property, an exterior angle of a triangle equals the sum of its two interior opposite angles.
Fill in the Blanks
Q1: A line segment drawn from any vertex of the triangle to the mid-point of the opposite side is called a _____.
Solution:
Ans: median
Q2: An altitude of a triangle is a _____ line segment that joins a vertex to the opposite side.
Solution:
Ans: perpendicular
Q3: In an isosceles triangle, _____ sides are of equal length.
Solution:
Ans: two
Q4: According to Pythagoras theorem, (Perpendicular)² + (Base)² = _____.
Solution:
Ans: (Hypotenuse)²
Q5: A triangle with one angle greater than 90° is called a _____ triangle.
Solution:
Ans: obtuse-angled
True or False
Q1: A triangle has three vertices, three sides, and three angles.
Solution:
Ans: True A triangle is defined by having three vertices where sides meet, three sides as line segments, and three angles.
Q2: In a scalene triangle, all sides are of equal length.
Solution:
Ans: False A scalene triangle has all sides of different lengths. An equilateral triangle has all sides of equal length.
Q3: A perpendicular bisector is perpendicular to a segment at its midpoint.
Solution:
Ans: True A perpendicular bisector is defined as a line that is perpendicular to a segment at its exact midpoint.
Q4: The sum of any two sides of a triangle is always less than the third side.
Solution:
Ans: False The sum of any two sides of a triangle must be greater than the third side for the triangle to exist.
Q5: Each angle in an equilateral triangle measures 60°.
Solution:
Ans: True In an equilateral triangle, all three angles are equal and each angle measures exactly 60 degrees.
Match the Following
Column A
Column B
1. Median of a triangle
A. Triangle with two equal sides
2. Equilateral triangle
B. Line segment from vertex perpendicular to opposite side
3. Isosceles triangle
C. Triangle with all angles less than 90°
4. Altitude of a triangle
D. Line segment from vertex to midpoint of opposite side
5. Acute-angled triangle
E. Triangle with all three equal sides
Solution:
Ans:
1 - D: A median is a line segment drawn from any vertex to the midpoint of the opposite side.
2 - E: An equilateral triangle has all three sides of equal length and all angles equal to 60°.
3 - A: An isosceles triangle has two sides of equal length and angles opposite to equal sides are equal.
4 - B: An altitude is a perpendicular line segment joining a vertex to the opposite side of the triangle.
5 - C: An acute-angled triangle has all three angles measuring less than 90 degrees.
Short Answer Questions
Q1: What is a triangle? Describe its basic components.
Solution:
Ans: A triangle is a simple closed figure made up of three straight line segments. It has three vertices, which are the points where the sides meet. It has three sides, which are the line segments forming the triangle. It also has three angles, which are the spaces between the sides. Triangles are common geometrical shapes used in everyday life.
Q2: Explain the difference between a median and an altitude of a triangle.
Solution:
Ans: A median is a line segment drawn from any vertex of the triangle to the midpoint of the opposite side. An altitude is a perpendicular line segment that joins a vertex to the opposite side. The median divides the opposite side into two equal parts, while the altitude forms a right angle with the opposite side. Both can be drawn from each vertex.
Q3: State and explain the exterior angle property of a triangle.
Solution:
Ans: An exterior angle of a triangle is formed when one side is extended. The exterior angle property states that an exterior angle equals the sum of its two interior opposite angles. For example, if we extend side BC to D in triangle ABC, the exterior angle at C equals the sum of angles at A and B. This property is useful for solving triangle problems.
Q4: How can you verify whether three given side lengths can form a triangle?
Solution:
Ans: To verify if three sides can form a triangle, check if the sum of any two sides is greater than the third side. This must be true for all three combinations of sides. Alternatively, check if the difference of any two sides is less than the third side. If either condition is satisfied for all combinations, the triangle can be formed.
Q5: What are the characteristics of an isosceles triangle?
Solution:
Ans: An isosceles triangle is a triangle in which two sides are of equal length. The angles opposite to the equal sides are also equal. This property helps in solving problems involving isosceles triangles. For example, if two sides are equal, their opposite angles are automatically equal. Isosceles triangles have a line of symmetry passing through one vertex.
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