Triangles Quiz - CBSE Class 10 Mathematics
Free practice quiz: Triangles (CBSE Class 10 Mathematics). 19 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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In a right triangle, what is the sum of all angles?
- 180 degrees
- 90 degrees
- 270 degrees
- 360 degrees
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Answer: A. 180 degrees
The sum of all angles in any triangle is always 180 degrees. In a right triangle, one angle is 90 degrees, and the other two angles add up to 90 degrees.
If two sides of a triangle are 8 cm and 15 cm, what could be the length range for the third side?
- Between 7 cm and 23 cm
- Between 5 cm and 20 cm
- Any value
- Exactly 23 cm
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Answer: A. Between 7 cm and 23 cm
By the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For this triangle, the possible range for the third side is (15 - 8) < x < (15 + 8), which simplifies to 7 < x < 23.
How many lines of symmetry does an equilateral triangle have?
- 1
- 2
- 3
- 4
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Answer: C. 3
An equilateral triangle has three sides of equal length and three angles of equal measure, resulting in three lines of symmetry.
What is the relationship between the circumcenter and the vertices of a triangle?
- It is equidistant from all three vertices.
- It is twice the distance from the longest side.
- It is closest to the largest angle.
- It is halfway between the orthocenter and incenter.
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Answer: A. It is equidistant from all three vertices.
The circumcenter of a triangle is equidistant from all its vertices, as it is the center of the circle circumscribing the triangle (circumcircle).
Solve for x: An isosceles triangle with one angle 40°.
- x = 40°
- x = 70°
- x = 140°
- x = 50°
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Answer: B. x = 70°
In an isosceles triangle, the angles opposite the equal sides are equal. If one angle is given as 40°, then the other two angles sum to 140° (since total is 180°). Therefore, x = 70°.