Class 9 Maths Chapter 5 HOTS Questions - Introduction to Euclid’s Geometry

Q1: Show that : length AH > sum of lengths of AB + BC + CD.Sol:
We have
AH = AB + BC + CD + DE + EF + FG + GH
Clearly, AB + BC + CD is a part of AH.
⇒ AH > AB + BC + CD
Hence, length AH > sum of lengths AB + BC + CD.

Q2: For given four distinct points in a plane, find the number of lines that can be drawn through :
(i) When all four points are collinear.
(ii) When three of the four points are collinear.
(iii) When no three of the four points are collinear.
Sol:

(i) Consider the points given are A, B, C and D.
When all the four points are collinear :
One line

(ii) When three of the four points are collinear :
4 lines
Here, we have four lines  (Four)
(iii) When no three of the four points are collinear :
6 lines Here, we have
 (Six)

Q3: Three lighthouse towers are located at points A, B and C on the section of a national forest to protect animals from hunters by the forest department as shown in figure. Which value is department exhibiting by locating extra towers ? How many straight lines can be drawn from A to C? State the Euclid Axiom which states the required result. Give one more. Postulate.
Sol: One and only one line can be drawn from A to C. According to Euclid’s Postulate, “A straight line may be drawn from any point to any other point:” An other postulate : “A circle may be described with any centre and any radius.” Wildlife is a part of our environment and conservation of each of its element is important for ecological balance.

Q4: Rohan’s maid has two children of same age. Both of them have equal number of dresses. Rohan on his birthday plans to give both of them same number of dresses. What can you say about the number of dresses each one of them will have after Rohan’s birthday? Which Euclid’s axiom is used to answer this question? What value is Rohan depicting by doing so ? Write one more Euclid’s axiom.
Sol: Here, Rohan’s maid has two children of same age group and both of them have equal number of dresses. Rohan on his birthday plans to give both of them same number of dresses.
∴ By using Euclid’s Axiom 2, if equals are added to equals, then the whole are equal.
Thus, again both of them have equal number of dresses.
Value depicted by Rohan are caring and other social values.
According to Euclid’s Axiom 3, if equals are subtracted from equals, then the remainders are equal.