Could You Actually Pass This Geometry Trivia Test?
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The sum of all the angles of a triangle is:
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90o
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180o
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270o
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360o
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About This Quiz
Could You Actually Pass This Geometry Trivia Test? There are a lot of people who are quite negative when it comes to geometry. Some even believe that only a few can solve some problems. Which team do you identify with? The quiz below is perfect for perfecting your geometry skills. Do give it a shot and get as much practice See moreas you need.
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- 2.
The exterior angle of a triangle is equal to___:
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Sum of all the angles in a triangle
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Sum of vertically opposite angles
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Sum of opposite interior angles in a triangle
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None of these
Correct Answer
A. Sum of vertically opposite anglesExplanation
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Vertically opposite angles are formed when two lines intersect, and they are equal in measure. Therefore, the sum of the vertically opposite angles is equal to the exterior angle of a triangle.Rate this question:
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- 3.
What would be the distance between the point of intersection of the two tangents and the centre of the circle, if a circle of radius 6 cm is constructed from which two tangents are arise which are inclined at an angle of 60o.
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15
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14
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13
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12
Correct Answer
A. 12Explanation
The distance between the point of intersection of the two tangents and the center of the circle can be found using the formula for the length of a radius of a circle inscribed in an equilateral triangle. In this case, the angle between the two tangents is 60 degrees, which means that the triangle formed by the center of the circle and the two points of intersection of the tangents is an equilateral triangle. The formula for the length of the radius of an inscribed equilateral triangle is r = s√3, where r is the radius of the circle and s is the length of each side of the equilateral triangle. In this case, the radius of the circle is 6 cm, so the length of each side of the equilateral triangle is 6 cm. Therefore, the distance between the point of intersection of the tangents and the center of the circle is 6√3 cm, which is approximately equal to 10.39 cm.Rate this question:
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- 4.
To divide a line segment AB in the ratio 3 : 7, first a ray AX is drawn so that angle BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is
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3
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7
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10
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12
Correct Answer
A. 10Explanation
To divide a line segment AB in the ratio 3:7, a ray AX is drawn from point A such that angle BAX is an acute angle. Then, points are marked on the ray AX at equal distances. The minimum number of these points required is 10. This is because the ratio 3:7 can be simplified to 3/10:7/10, indicating that the line segment AB needs to be divided into 10 equal parts. Therefore, 10 points are marked on the ray AX to divide the line segment AB in the desired ratio.Rate this question:
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- 5.
To divide a line segment AB in the ratio 4 : 5, a ray AX is drawn first such that angle BAX is an acute angle and then points A1, A2, A3,…. are located at equal distances on the ray AX and the point B is joined to:
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A4
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A5
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A9
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A10
Correct Answer
A. A9Explanation
In order to divide a line segment AB in the ratio 4:5, a ray AX is drawn first such that angle BAX is an acute angle. Then, points A1, A2, A3,... are located at equal distances on the ray AX. Since the ratio is 4:5, it means that the line segment AB is divided into 4 parts by the points A1, A2, A3,..., and B is joined to the 9th point, which is A9. Therefore, the correct answer is A9.Rate this question:
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- 6.
To divide a line segment AB in the ratio 4 : 5, draw a ray AX such that angle BAX is an acute angle, then draw a ray BY parallel to AX and the points A1, A2, A3, and B1, B2, B3.... are located at equal distances n ray AX and BY, respectively. Then the points joined are:
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A4 and B5
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A5 and B4
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A5 and B6
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A6 and B6
Correct Answer
A. A4 and B5Explanation
The question states that to divide the line segment AB in the ratio 4:5, we need to draw a ray AX such that angle BAX is an acute angle. Then, a ray BY parallel to AX is drawn. The points A1, A2, A3... are located at equal distances on ray AX, and the points B1, B2, B3... are located at equal distances on ray BY. According to the given information, the points A4 and B5 are joined. Therefore, the correct answer is A4 and B5.Rate this question:
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- 7.
To construct a triangle similar to a given ΔABC with its sides 2/5 of the corresponding sides of ΔABC, first draw a ray BX such that angle CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1, B2, B3,..... on BX at equal distances and next step is to join:
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B2 to C
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B3 to C
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B4 to C
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B5 to C
Correct Answer
A. B5 to CExplanation
In order to construct a triangle similar to triangle ABC with its sides 2/5 of the corresponding sides of triangle ABC, we start by drawing a ray BX such that angle CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then, we locate points B1, B2, B3, ... on BX at equal distances. The next step is to join B5 to C. This step completes the construction of the triangle similar to triangle ABC with its sides 2/5 of the corresponding sides of triangle ABC.Rate this question:
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- 8.
To construct a triangle similar to a given ΔABC with its sides 5/3 of the corresponding sides of ΔABC draw a ray BX such that CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is
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2
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3
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5
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8
Correct Answer
A. 3Explanation
To construct a triangle similar to a given ΔABC with its sides 5/3 of the corresponding sides of ΔABC, we need to draw a ray BX such that CBX is an acute angle and X is on the opposite side of A with respect to BC. In order to locate points at equal distances on ray BX, we need at least three points. This is because with two points, we can only determine a line segment, but with three points, we can determine a ray. Therefore, the minimum number of points to be located at equal distances on ray BX is 3.Rate this question:
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- 9.
To draw a pair of tangents to circle which are inclined to each other at an angle of 30°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be :
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60o
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90o
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120o
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150o
Correct Answer
A. 150oExplanation
To draw a pair of tangents to a circle that are inclined to each other at an angle of 30°, we need to draw tangents at the end points of two radii of the circle. The angle between these two tangents can be found by subtracting the given angle of 30° from 180° (since the sum of angles in a straight line is 180°). Therefore, the angle between the two tangents should be 180° - 30° = 150°.Rate this question:
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- 10.
P3 divides the line segment AP in the ratio:
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2 : 3
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4 : 1
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1 : 4
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3 : 2
Correct Answer
A. 3 : 2Explanation
P3 divides the line segment AP in the ratio 3:2. This means that P3 divides the line segment into two parts, where the length of the first part is 3 times the length of the second part. In other words, if the total length of the line segment AP is 'x', then the length of the first part is (3/5)x and the length of the second part is (2/5)x.Rate this question:
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- 11.
What ratio does the line segment A3B2 represent in the following figure:
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3 : 2
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2 : 3
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Both (a) & (b)
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Neither (a) & (b)
Correct Answer
A. 3 : 2Explanation
The line segment A3B2 represents the ratio 3:2. This means that the length of A3B2 is three times the length of A1A2 and two times the length of A2B1.Rate this question:
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- 12.
The scale factor means:
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The ratio of angles of the triangle to be constructed with the corresponding angle of the given triangle
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The ratio of sides of the triangle to be constructed with the corresponding sides of the given triangle
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Both (a) & (b)
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Neither (a) & (b)
Correct Answer
A. The ratio of sides of the triangle to be constructed with the corresponding sides of the given triangleExplanation
The correct answer is "Both (a) & (b)". The scale factor refers to the ratio of both the angles and the sides of the triangle to be constructed with the corresponding angles and sides of the given triangle. In other words, it encompasses both the ratio of angles and the ratio of sides.Rate this question:
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- 13.
If two tangents are drawn at the end points of two radii of a circle which are inclined at 130o to each other, then the pair of tangents will be inclined to each other at an angle of:
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40o
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50o
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60o
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70o
Correct Answer
A. 50oExplanation
When two tangents are drawn at the end points of two radii of a circle, they intersect at a point on the circumference of the circle. This forms an isosceles triangle with the radii as the equal sides. Since the radii are inclined at 130o to each other, the angle between the tangents is half of the angle between the radii. Therefore, the angle between the tangents is 130o/2 = 65o. However, the question asks for the angle between the tangents, not the angle between the radii. Since the angle between the tangents is the exterior angle of the triangle, the angle between the tangents is 180o - 65o = 115o. However, this is the exterior angle, so the angle between the tangents is 180o - 115o = 65o. Therefore, the correct answer is 50o.Rate this question:
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- 14.
Two circles touch each other externally at Q and PR is a common tangent to the circles. Then, ∠PQR is:
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0o
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90o
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180o
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360o
Correct Answer
A. 90oExplanation
When two circles touch each other externally, the point of contact is the only point where the circles intersect. In this case, the common tangent PR is perpendicular to the line joining the centers of the circles, since the tangent is always perpendicular to the radius at the point of contact. Therefore, the angle PQR formed at the point of contact Q is a right angle, measuring 90 degrees.Rate this question:
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- 15.
To draw a pair of tangents to a circle which is at right angles to each other, it is required to draw tangents at endpoints of the two radii of the circle, which are inclined at an angle of:
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60o
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80o
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90o
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120o
Correct Answer
A. 90oExplanation
To draw a pair of tangents to a circle that are at right angles to each other, it is necessary to draw tangents at the endpoints of the two radii of the circle. Since the radii of a circle are always perpendicular to the tangent at the point of contact, the angle between the two radii is 90 degrees. Therefore, the correct answer is 90o.Rate this question:
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Quiz Review Timeline (Updated): Nov 16, 2023 +
Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.
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Current Version
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Nov 16, 2023Quiz Edited by
ProProfs Editorial Team -
Dec 20, 2013Quiz Created by
Tanmay Shankar
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