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Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
parallel lines
Concept: undefined >> undefined
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
perpendicular lines
Concept: undefined >> undefined
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Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
line segment
Concept: undefined >> undefined
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
radius of a circle
Concept: undefined >> undefined
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
square
Concept: undefined >> undefined
Consider two ‘postulates’ given below:-
- Given any two distinct points A and B, there exists a third point C which is in between A and B.
- There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.
Concept: undefined >> undefined
If a point C lies between two points A and B such that AC = BC, then prove that AC = `1/2` AB. Explain by drawing the figure.
Concept: undefined >> undefined
If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
Concept: undefined >> undefined
In the following figure, if AC = BD, then prove that AB = CD.
Concept: undefined >> undefined
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)
Concept: undefined >> undefined
Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels.
Concept: undefined >> undefined
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Concept: undefined >> undefined
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Concept: undefined >> undefined
There is a slide in the park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.
Concept: undefined >> undefined
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Concept: undefined >> undefined
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Concept: undefined >> undefined
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Concept: undefined >> undefined
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f ( x ) = 3x +1, x = - 1/3`
Concept: undefined >> undefined
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f(x)=x^2- 1,x=1,-1`
Concept: undefined >> undefined
In Fig. 10.22, the sides BA and CA have been produced such that: BA = AD and CA = AE.
Prove that segment DE || BC.
Concept: undefined >> undefined
