Question

the construction of a triangle DEF in which DE is 7 cm Angle D is 75 degree is possible when DE - EF is equal to​ ___________^^^

Answer 1

$\triangle EFD$ is the required triangle.

Step-by-step explanation:

Given,

Construction of  in which $\triangle EFD$ where $DE=7\ cm$ 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

DEF is the required triangle

Step-by-step explanation:

given : To construct triangle DEF in  which DE = 7 cm and angle D is 75 degrees

since ,

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

DF-EF < 7

therefore we can take the value of  DF - EF is 6.5 CM

steps for construction :

1. Draw line segments  DE = 7 cm
2. At D, draw an angle 75 degree
3. Cuts a point P on line DX , DP = 6.5 cm
4. Join PE
5. Bisect the line PE and the bisecting line cuts the DX at F
6. Join EF
7. DEF is the required triangle

#Learn more:

Construct a triangle DEF in which DE= EF=5 cm and angle E=30 degree. Measure angle D and angle E.

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