Class 9 Math, Euclid's Geometry Dear Class 9 students and fellow educators, 'Jsunil Sir' welcomes you to an enlightening journey into the world of Euclid's Geometry at JSUNIL TUTORIAL. This comprehensive guide offers a clear and easy-to-understand introduction to the principles laid down by the ancient mathematician Euclid. Whether you're a budding learner or a dedicated teacher, this resource is designed to deepen your understanding of geometry. Explore the foundations, sharpen your math skills, and lay a strong groundwork for academic success. Dive into Euclid's Geometry with us today EUCLID’S Postulates 1. A straight line may be drawn from any point to any other point. 2. A terminated line (line segment) can be produced indefinitely. 3. A circle may be described with any centre and any radius. 4. All right angles are equal to one another. 5. If a straight line falling on two straight lines makes the interior angles on the same side of it, taken together less than two right angles, then the the two straight lines if produced indefinitely, meet on that side on which the sum of angles is taken together less than two right angles. Euclid used the term postulate for the assumptions that were specific to geometry and otherwise called axioms. A theorem is a mathematical statement whose truth has been logically established. Visit Page Link to download solved Questions and Guess test Paper CBSE Class IX Introduction to Euclid's geometry Q.1. If a point C lies between two points A and B such that AC = BC, then prove that AC =1/2AB.
Solution. According to the given statement, the figure will be as shown alongside in which the point C lies between two points A and B such that AC = BC. Clearly, AC + BC = AB AC + AC = AB [AC = BC] 2AC = AB And, AC = ½ AB Q.2. How would you rewrite Euclid’ fifth postulate so that it would be easier to understand? Solution: Two distinct intersecting lines cannot be parallel to the same line. Q.3. Does Euclid’s fifth postulate imply the existence of parallel lines ? Explain. Solution : if a straight line l falls on two straight lines m and n such that sum of the interior angles on one side of l is two right angles, then by Euclid’s fifth postulate the line will not meet on this side of l . Next, we know that the sum of the interior angles on the other side of line l also be two right angles. Therefore they will not meet on the other side. So, the lines m and n never meet and are, therefore parallel. Q.4. If lines AB, AC, AD and AE are parallel to a line l , then points A, B, C, D and E are collinear. Solution: Given : Lines AB, AC, AD and AE are parallel to a line l . To prove : A, B, C, D, E are collinear. Proof : Since AB, AC, AD and AE are all parallel to a line l Therefore point A is outside and lines AB, AC, AD, AE are drawn through A and each line is parallel to l . But by parallel lines axiom, one and only one line can be drawn through the point A outside it and parallel to l . This is possible only when A, B, C, D, and E all lie on the same line. Hence, A, B, C, D and E are collinear. Q.5. we have: AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using an Euclid’s axiom, show that AB = XY. Solution : AB = 2AC (C is the mid-point of AB) and XY = 2XD (D is the mid-point of XY) Also, AC = XD (Given) Therefore, AB = XY, because things which are double of the same things are equal to one another. Download pdf
1 Comment
summi
29/8/2012 01:18:53 pm
Euclid’s fifth postulate: If a straight line falling on two straight lines forms the interior angles that together measure less than two right angles on the same side of it, then the two straight lines, if produced indefinitely, meet on that side on which the sum of the angles is less than two right angles.
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