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All questions of Triangles, and Quadrilateral for Class 6 Exam
Which of the following correctly describes an acute-angled triangle?- a) One angle is equal to 90 degrees.
- b) Two angles are equal.
- c) One angle is greater than 90 degrees.
- d) All angles are less than 90 degrees.
Correct answer is option 'D'. Can you explain this answer?
Which of the following correctly describes an acute-angled triangle?
a)
One angle is equal to 90 degrees.
b)
Two angles are equal.
c)
One angle is greater than 90 degrees.
d)
All angles are less than 90 degrees.
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An acute-angled triangle is characterized by having all three angles measuring less than 90 degrees. This classification is essential in understanding the properties of triangles.
If a triangle has two sides of equal length, which type of triangle is it?- a) Right
- b) Isosceles
- c) Scalene
- d) Equilateral
Correct answer is option 'B'. Can you explain this answer?
If a triangle has two sides of equal length, which type of triangle is it?
a)
Right
b)
Isosceles
c)
Scalene
d)
Equilateral
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A triangle with two sides of equal length is classified as an isosceles triangle. This type of triangle has the property that the angles opposite the equal sides are also equal.
What is the sum of the interior angles of a triangle?- a) 180 degrees
- b) 360 degrees
- c) 270 degrees
- d) 90 degrees
Correct answer is option 'A'. Can you explain this answer?
What is the sum of the interior angles of a triangle?
a)
180 degrees
b)
360 degrees
c)
270 degrees
d)
90 degrees
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Mahesh Chavan answered |
Understanding the Sum of Interior Angles in a Triangle
The sum of the interior angles of a triangle is a fundamental concept in geometry. Let's break down why this is the case.
What is a Triangle?
- A triangle is a polygon with three edges and three vertices.
- The angles inside the triangle are known as interior angles.
Sum of Interior Angles
- The sum of the interior angles of any triangle is always 180 degrees.
- This can be visualized by drawing a triangle and extending one of its sides.
Visual Explanation
- When you draw a triangle, if you draw a line parallel to one of its sides through the opposite vertex, it creates alternate interior angles with the angles at the endpoints of the triangle.
- The two angles formed with the parallel line and the other two sides of the triangle will add to 180 degrees.
Types of Triangles
- Whether it is an equilateral triangle (all angles equal), isosceles triangle (two angles equal), or a scalene triangle (all angles different), the sum remains constant at 180 degrees.
Conclusion
- Therefore, the correct answer to the question regarding the sum of the interior angles of a triangle is option 'A' – 180 degrees.
Understanding this principle helps in solving various geometry problems involving triangles and is foundational for more complex shapes and polygons.
The sum of the interior angles of a triangle is a fundamental concept in geometry. Let's break down why this is the case.
What is a Triangle?
- A triangle is a polygon with three edges and three vertices.
- The angles inside the triangle are known as interior angles.
Sum of Interior Angles
- The sum of the interior angles of any triangle is always 180 degrees.
- This can be visualized by drawing a triangle and extending one of its sides.
Visual Explanation
- When you draw a triangle, if you draw a line parallel to one of its sides through the opposite vertex, it creates alternate interior angles with the angles at the endpoints of the triangle.
- The two angles formed with the parallel line and the other two sides of the triangle will add to 180 degrees.
Types of Triangles
- Whether it is an equilateral triangle (all angles equal), isosceles triangle (two angles equal), or a scalene triangle (all angles different), the sum remains constant at 180 degrees.
Conclusion
- Therefore, the correct answer to the question regarding the sum of the interior angles of a triangle is option 'A' – 180 degrees.
Understanding this principle helps in solving various geometry problems involving triangles and is foundational for more complex shapes and polygons.
How many diagonals does a quadrilateral have?- a) 4
- b) 2
- c) 5
- d) 3
Correct answer is option 'B'. Can you explain this answer?
How many diagonals does a quadrilateral have?
a)
4
b)
2
c)
5
d)
3
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Ashwini Goyal answered |
Understanding Diagonals in a Quadrilateral
A quadrilateral is a polygon with four sides. To find the number of diagonals in a quadrilateral, we can use a simple formula or visualize it.
What is a Diagonal?
- A diagonal is a line segment that connects two non-adjacent vertices (corners) of a polygon.
Counting the Diagonals in a Quadrilateral
- In a quadrilateral, there are four vertices. Let's label them as A, B, C, and D.
- The diagonals can be drawn between the following pairs of vertices:
- A to C
- B to D
Visualizing the Diagonals
- If you draw a quadrilateral, you will see that:
- Diagonal 1: A to C
- Diagonal 2: B to D
- Therefore, there are a total of 2 diagonals in a quadrilateral.
Formula for Diagonals
- For any polygon with 'n' sides, the formula to calculate the number of diagonals is:
- (n * (n - 3)) / 2
- For a quadrilateral (n = 4):
- (4 * (4 - 3)) / 2 = (4 * 1) / 2 = 2
Conclusion
- Hence, the correct answer is option 'B', which states that a quadrilateral has 2 diagonals.
Understanding this concept is crucial as it forms the basis for studying more complex polygons and their properties in geometry.
A quadrilateral is a polygon with four sides. To find the number of diagonals in a quadrilateral, we can use a simple formula or visualize it.
What is a Diagonal?
- A diagonal is a line segment that connects two non-adjacent vertices (corners) of a polygon.
Counting the Diagonals in a Quadrilateral
- In a quadrilateral, there are four vertices. Let's label them as A, B, C, and D.
- The diagonals can be drawn between the following pairs of vertices:
- A to C
- B to D
Visualizing the Diagonals
- If you draw a quadrilateral, you will see that:
- Diagonal 1: A to C
- Diagonal 2: B to D
- Therefore, there are a total of 2 diagonals in a quadrilateral.
Formula for Diagonals
- For any polygon with 'n' sides, the formula to calculate the number of diagonals is:
- (n * (n - 3)) / 2
- For a quadrilateral (n = 4):
- (4 * (4 - 3)) / 2 = (4 * 1) / 2 = 2
Conclusion
- Hence, the correct answer is option 'B', which states that a quadrilateral has 2 diagonals.
Understanding this concept is crucial as it forms the basis for studying more complex polygons and their properties in geometry.
What defines a regular polygon?- a) No sides are equal.
- b) All sides are equal, but angles are not.
- c) All sides are equal and angles are equal.
- d) Sides can be of different lengths.
Correct answer is option 'C'. Can you explain this answer?
What defines a regular polygon?
a)
No sides are equal.
b)
All sides are equal, but angles are not.
c)
All sides are equal and angles are equal.
d)
Sides can be of different lengths.
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A regular polygon is defined by having all sides and all angles equal. This symmetry is what differentiates regular polygons from irregular ones.
Which type of triangle has one angle that is greater than 90 degrees?- a) Acute Triangle
- b) Obtuse Triangle
- c) Right Triangle
- d) Isosceles Triangle
Correct answer is option 'B'. Can you explain this answer?
Which type of triangle has one angle that is greater than 90 degrees?
a)
Acute Triangle
b)
Obtuse Triangle
c)
Right Triangle
d)
Isosceles Triangle
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An obtuse triangle is characterized by having one angle that is greater than 90 degrees. This distinguishes it from acute triangles, which have all angles less than 90 degrees, and right triangles, which have one angle equal to 90 degrees.
A quadrilateral with opposite sides that are both parallel and equal in length is known as a:- a) Square
- b) Trapezium
- c) Rectangle
- d) Parallelogram
Correct answer is option 'D'. Can you explain this answer?
A quadrilateral with opposite sides that are both parallel and equal in length is known as a:
a)
Square
b)
Trapezium
c)
Rectangle
d)
Parallelogram
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A parallelogram is defined as a quadrilateral where both pairs of opposite sides are parallel and equal in length. This property is fundamental to its classification among quadrilaterals.
What is the term for the point where all three medians of a triangle intersect?- a) Orthocenter
- b) Incenter
- c) Circumcenter
- d) Centroid
Correct answer is option 'D'. Can you explain this answer?
What is the term for the point where all three medians of a triangle intersect?
a)
Orthocenter
b)
Incenter
c)
Circumcenter
d)
Centroid
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The centroid is the point where all three medians of a triangle intersect. It is also the center of mass of the triangle, providing a unique balance point for the shape.
In triangle PQR, if side PQ is extended to form an exterior angle, which of the following statements is true?- a) The exterior angle is equal to the sum of angles P and R.
- b) The exterior angle is equal to angle Q.
- c) The exterior angle is less than angle R.
- d) The exterior angle is equal to angle R.
Correct answer is option 'A'. Can you explain this answer?
In triangle PQR, if side PQ is extended to form an exterior angle, which of the following statements is true?
a)
The exterior angle is equal to the sum of angles P and R.
b)
The exterior angle is equal to angle Q.
c)
The exterior angle is less than angle R.
d)
The exterior angle is equal to angle R.
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The exterior angle formed by extending side PQ is equal to the sum of the two opposite interior angles, angles P and R. This relationship is fundamental in understanding triangle properties.
In a triangle, what is the term used for a line segment drawn from a vertex perpendicular to the opposite side?- a) Altitude
- b) Bisector
- c) Median
- d) Segment
Correct answer is option 'A'. Can you explain this answer?
In a triangle, what is the term used for a line segment drawn from a vertex perpendicular to the opposite side?
a)
Altitude
b)
Bisector
c)
Median
d)
Segment
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An altitude is defined as a line segment that is drawn from a vertex of a triangle perpendicular to the opposite side. This property is essential in calculating the area of the triangle.
What is the main characteristic of a rectangle?- a) Diagonals are equal and intersect at right angles.
- b) Opposite sides are equal and all angles are 90 degrees.
- c) All sides are equal.
- d) Only one pair of sides is parallel.
Correct answer is option 'B'. Can you explain this answer?
What is the main characteristic of a rectangle?
a)
Diagonals are equal and intersect at right angles.
b)
Opposite sides are equal and all angles are 90 degrees.
c)
All sides are equal.
d)
Only one pair of sides is parallel.
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A rectangle is characterized by having opposite sides that are equal and all interior angles measuring 90 degrees. This property ensures that rectangles are a specific type of parallelogram.
Which of the following is a property of an isosceles triangle?- a) Contains a right angle.
- b) All angles are acute.
- c) Two sides are equal.
- d) All sides are equal.
Correct answer is option 'C'. Can you explain this answer?
Which of the following is a property of an isosceles triangle?
a)
Contains a right angle.
b)
All angles are acute.
c)
Two sides are equal.
d)
All sides are equal.
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An isosceles triangle is defined by having two sides that are equal in length. This characteristic also implies that the angles opposite these equal sides are equal, which is a key property of isosceles triangles.
Which of the following shapes is classified as a polygon?- a) A triangle
- b) A wave
- c) A circle
- d) A curve
Correct answer is option 'A'. Can you explain this answer?
Which of the following shapes is classified as a polygon?
a)
A triangle
b)
A wave
c)
A circle
d)
A curve
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A polygon is defined as a closed shape formed by straight line segments that connect at their endpoints without crossing. Among the options, only a triangle fits this definition as it has three straight sides and is closed.
In triangle ABC, if angle A is extended to form an exterior angle, what is the relationship between the exterior angle and the two opposite interior angles?- a) They sum to 90 degrees.
- b) They sum to 180 degrees.
- c) They are equal.
- d) They are complementary.
Correct answer is option 'C'. Can you explain this answer?
In triangle ABC, if angle A is extended to form an exterior angle, what is the relationship between the exterior angle and the two opposite interior angles?
a)
They sum to 90 degrees.
b)
They sum to 180 degrees.
c)
They are equal.
d)
They are complementary.
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The exterior angle of a triangle is equal to the sum of the two opposite interior angles. This relationship is crucial in solving problems involving triangles and their angles.
What is a median of a triangle?- a) A perpendicular line from a vertex
- b) A segment bisecting an angle
- c) A line connecting two midpoints
- d) A segment from a vertex to the opposite side
Correct answer is option 'D'. Can you explain this answer?
What is a median of a triangle?
a)
A perpendicular line from a vertex
b)
A segment bisecting an angle
c)
A line connecting two midpoints
d)
A segment from a vertex to the opposite side
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A median is defined as a line segment that connects a vertex of the triangle to the midpoint of the opposite side. This segment divides the triangle into two smaller triangles of equal area.
What type of quadrilateral has two pairs of equal adjacent sides?- a) Parallelogram
- b) Trapezium
- c) Kite
- d) Rectangle
Correct answer is option 'C'. Can you explain this answer?
What type of quadrilateral has two pairs of equal adjacent sides?
a)
Parallelogram
b)
Trapezium
c)
Kite
d)
Rectangle
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A kite is defined by having two pairs of adjacent sides that are equal in length. This unique shape also has one pair of opposite angles that are equal, which distinguishes it from other quadrilaterals.
Which quadrilateral has all sides of equal length and all angles equal to 90 degrees?- a) Rhombus
- b) Parallelogram
- c) Rectangle
- d) Square
Correct answer is option 'D'. Can you explain this answer?
Which quadrilateral has all sides of equal length and all angles equal to 90 degrees?
a)
Rhombus
b)
Parallelogram
c)
Rectangle
d)
Square
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A square is a special type of quadrilateral that has all sides of equal length and all angles measuring 90 degrees. This makes it a unique and regular quadrilateral.
What type of triangle has all three sides of equal length?- a) Isosceles Triangle
- b) Equilateral Triangle
- c) Right-Angled Triangle
- d) Scalene Triangle
Correct answer is option 'B'. Can you explain this answer?
What type of triangle has all three sides of equal length?
a)
Isosceles Triangle
b)
Equilateral Triangle
c)
Right-Angled Triangle
d)
Scalene Triangle
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An equilateral triangle is characterized by having all three sides equal in length and all angles measuring 60 degrees. This property distinguishes it from isosceles and scalene triangles, which have different side lengths.
A trapezium with non-parallel sides that are equal in length is specifically called:- a) Right Trapezium
- b) Scalene Trapezium
- c) Isosceles Trapezium
- d) Rectangular Trapezium
Correct answer is option 'C'. Can you explain this answer?
A trapezium with non-parallel sides that are equal in length is specifically called:
a)
Right Trapezium
b)
Scalene Trapezium
c)
Isosceles Trapezium
d)
Rectangular Trapezium
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An isosceles trapezium is defined by having one pair of non-parallel sides that are equal in length. This property distinguishes it from other trapeziums.
In a trapezium, how many sides are parallel?- a) One
- b) Three
- c) Two
- d) None
Correct answer is option 'A'. Can you explain this answer?
In a trapezium, how many sides are parallel?
a)
One
b)
Three
c)
Two
d)
None
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A trapezium (or trapezoid in some regions) is defined as a quadrilateral that has at least one pair of parallel sides. This defining property distinguishes trapeziums from other types of quadrilaterals.
Chapter doubts & questions for Triangles, and Quadrilateral - Mathematics Class 6 ICSE 2025 is part of Class 6 exam preparation. The chapters have been prepared according to the Class 6 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 6 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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Mathematics Class 6 ICSE
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