Question

Hi can someone please help me with this geometry problem? Thanks!

Answer 1

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The triangles ΔEST and ΔEFD are similar triangles, therefore, we can write,

$\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}$

Since S and T are midpoints of EF and ED, the lines will be divided into two equal parts. Therefore,

$\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}= \dfrac12$

Therefore, we can write it as,

$FD = 2 (ST)$

In ΔEST and ΔTDR

∠T ≅ ∠T {Vertical angles}

ET ≅ TD {T is the midpoint of ED}

∠SET ≅ ∠TDR {Alternate interior angles}

Therefore,  ΔEST ≅ ΔTDR.

Since the two triangles are equal we can write,

ST ≅ TR

Further, it can be written as,

FD = 2(ST)

FD = ST + ST

FD = ST + TR

FD = SR

Hence, FD≅SR.

Learn more about Triangle:

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