Constructions of Class 9
Question
To construct a triangle, given its base, a base angle and difference of the other two sides.
Solution
Case 1 :
We shall construct ΔABC, when base BC, and ∠B are given. Also, we are given Here, AB > AC.
Steps of construction :
1. Draw the given base BC. 2. Construct ∠CBX = ∠B as given. 3. Along BX cut BD = AB − AC. (Here, BD and BA are in the same direction) 4. Join CD. 5. Construct the perpendicular bisector PQ of CD and PQ intersects CD at L and QP (produced) meets BX at A. 6. Join AC. Here, AC = AD |
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Hence the ΔABC is required triangle.
Justification :
In ΔACD, AL is perpendicular bisector of CD.
⇒ AC = AD.
Now, in ΔABC we have
Case 2 :
Let us construct ΔABC, when BC, and ∠B are given. Also, AC > AB, and AC − AB is given.
Steps of construction :
1. Draw the given base BC. 2. Construct ∠CBX = ∠B as given. 3. Cut BD = AC − AB along XB (Produced). Here, BD and BA are in the opposite directions. 4. Join CD. 5. Construct the perpendicular bisector PQ of CD. 6. QP meets BX at A and CD at L. 7. Join AC. Here, AC = AD = AB + BD i.e., AC − AB = BD. |
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Hence, ΔABC is the required triangle.
Justification :
In ΔACD, AL is perpendicular bisector of CD.
⇒ AC = AD.
Frequently Asked Questions
Which of the following rational numbers lies between 0 and - 1
A: 0
B: - 1
C: -1/4
D: 1/4
Solution:
Explanation:
0 and 1 cannot be found between 0 and 1.
In addition,0= o/4 and -1= -4/4
We can see that -1/4 is halfway between 0 and -1.
Final Answer:
Hence, the correct option is (c) -1/4
Prove that the diagonals of a parallelogram bisect each other
Solution:
Explanation:
We must show that the diagonals of the parallelogram ABCD cross each other.
OA = OC & OB = OD, in other words.
Now AD = BC [opposite sides are equal] in ΔAOD and ΔBOC.
[alternative interior angle] ∠ADO = ∠CBO in ΔAOD and ΔBOC.
Similarly, ∠AOD = ∠BOC by ΔDAO = ΔBCO (ASA rule)
As a result, OA = OC and OB = OB [according to CPCT].
Final Answer:
Hence, it is prove that the diagonals of a parallelogram bisect each other.
What is total surface area of sphere
Solution:
Explanation:
- The radius of the sphere affects the formula for calculating the sphere's surface area.
- If the sphere's radius is r and the sphere's surface area is S.
- The sphere's surface area is therefore stated as Surface Area of Sphere 4πr2, where ‘r’ is the sphere's radius.
- The surface area of a sphere is expressed in terms of diameter as S=4π(d/2)2, where d is the sphere's diameter.
Final Answer:
Thus, total surface area of sphere is =4πr2.
Fill in the blanks If two adjacent angles are supplementary
they form a __________.
Solution:
Explanation:
- If the non-common sides of two angles form a straight line, they are called linear pair angles.
- The sum of the angles of two linear pairs is degrees.
- If the total of two angles is degrees, they are called supplementary angles.
Final Answer:
A linear pair is formed.



