Question

The construction of triangle DEF in which DE=7 cm, angle D = 75° is possible when (DE-EF) is equal to how many centimeters

Answer 1

$\triangle EFD$ is the required triangle.

Step-by-step explanation:

Given,

Construction of $\triangle EFD$ in which $DE=7\ cm\ and\ \angle D = 75\ degree$

We know,

The construction of a triangle is not possible if sum of two sides is greater than third side of triangle.

$(DE+EF)>DF$

⇒$DE>(DF-EF)$

⇒ $7>(DF-EF)$

We can take the value of $(DF-EF)$ is $6.5\ cm$

Following steps:

• Draw line segments $DE=7\ cm$ using scale.
• At $D$, draw an angle $75\ degree$ like $\angle EDX=75\ degree$
• Cuts a point $P$ on line $DX$ like $DP=6.5\ cm$
• Join $PE$

• Bisect the line $PE$ and the bisecting line cuts the $DX$ at $F$
• Join $EF$

Hence, $\triangle EFD$ is the required triangle.

Answer 2

Answer:

Step-by-step explanation:

Step-by-step explanation:

Given,

Construction of  in which  

We know,

The construction of a triangle is not possible if sum of two sides is greater than third side of triangle.

⇒

⇒  

We can take the value of  is  

Following steps:

Draw line segments  using scale.

At , draw an angle  like  

Cuts a point  on line  like  

Join  

Bisect the line  and the bisecting line cuts the  at  

Join  

Hence,  is the required triangle.