Tag: construction of triangles - i

Questions Related to construction of triangles - i

Which of the following steps is INCORRECT, while constructing $\triangle$LMN, right angled at M, given that LN = 5 cm and MN = 3 cm?
Step 1. Draw MN of length 3 cm.
Step 2. At M, draw MX $\perp$ MN. (L should be some where on this perpendicular).
Step 3. With N as centre, draw an arc of radius 5 cm. (L must be on this arc, since it is at a distance of 5 cm from N).
Step 4. L has to be on the perpendicular line MX as well as on the arc drawn with centre N. Therefore, L is the meeting point of these two and $\triangle$LMN is obtained.

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. Only Step 4

  2. Both Step 2 and Step 3

  3. Only Step 2

  4. None of these

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Correct Option: A

In a right-angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $40^{\circ}$

  2. $42^{\circ}$

  3. $44^{\circ}$

  4. $45^{\circ}$

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Correct Option: D
Explanation:

In a right angled triangle, if the square of the hypotenuse is  equal to twice the product of  the other two sides, then the two angles are equal.
Since, one of the angle is 90, the sum of other two will be 90. 
Thus, each angle should be $45^{\circ}$