Question

The length of DE is shown. What other length can you determine for this diagram?

Answer 1

Answer: You can determine FE=DE=12 as other length from the given diagram

Explanation:

Let O be the intersecting point of the line segment GE and DF in the given figure.

Now, in triangle FED, we can say EO is perpendicular bisector of FD.

Since EO ⊥ FD and FO=OD

Therefore, in ΔFOE and ΔDOE

OE=OE [Common]

∠FOE=∠DOE [each right angle]

FO=DO [Given]

⇒ ΔFOE ≅ ΔDOE [By SAS congruence postulate]

⇒FE≅DE (by CPCT)

Since DE=12 [Given]

∴ FE=12

Thus, the other length we can determine for the given diagram is FE=12.

Answer 2

Another length of this diagram FE=12.

Explanation:

According to diagram

In triangle FED, EM is perpendicular bisector of FD.

In ΔFED, EM ⊥ FD and FM=MD

In ΔFME and ΔDME

FM=DM (Given)

∠FME=∠DME (each 90°)

ME=ME (Common)

ΔFME ≅ ΔDME (By SAS congruence property)

Therefore, FE≅DE (by CPCT)

But DE=12

So, FE=12

Thus, Another length of this diagram FE=12.