Introduction to Euclid's Geometry — Practice Quiz
Gujarat Board · Class 9 · Mathematics
Try a 4-question quiz on Introduction to Euclid's Geometry for Gujarat Board Class 9 Mathematics: tap an answer to check it and see why.
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Quick Quiz: Introduction to Euclid's Geometry
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If AB = 5 cm and BC = 3 cm, and point B lies between points A and C on a straight line, what is the length of AC?
In triangle ABC, if AB = 6 cm, BC = 6 cm, and AC = 6 cm, what type of triangle is it?
If two circles have radii of 4 cm and 7 cm respectively, and they intersect at point P, what can we say about the distances AP and BP where A and B are the centers?
Using Euclid's construction method, what is the first step to construct an equilateral triangle on a given line segment AB?
Sample Questions
Which of the following statements about Euclid's axioms are correct?
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Things equal to the same thing are equal to one another, If equals are added to equals, the wholes are equal, The whole is greater than the part
These are three of Euclid's fundamental axioms. Option 3 is incorrect because all right angles are equal (this is actually Postulate 4). Option 5 is incorrect because Postulate 3 states a circle can be drawn with any center and any radius.
If AC = BD in the figure where points are arranged as A-B-C-D on a line, what is the relationship between AB and CD?
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AB = CD
Given AC = BD, we can write AC = AB + BC and BD = BC + CD. Since AC = BD, we have AB + BC = BC + CD. Using Euclid's axiom 'if equals are subtracted from equals, the remainders are equal', subtracting BC from both sides gives AB = CD.
Which of the following are undefined terms in Euclid's geometry?
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Point, Line, Plane
Point, line, and plane are taken as undefined terms in Euclid's geometry because attempting to define them leads to circular definitions. Triangle and circle can be defined using these undefined terms and other geometric concepts.
If a line segment PQ is 10 cm long and point R is the midpoint of PQ, what is the length of PR?
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5 cm
Since R is the midpoint of PQ, it divides PQ into two equal parts. Therefore, PR = RQ = PQ/2 = 10/2 = 5 cm. This follows from the definition of a midpoint and the axiom that the whole equals the sum of its parts.
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