The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
What is Kite?
A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.
Given,
ABCD is a kite, with the diagonal AD and BC
We have,
AC = AB
and
CD = BD [Property of Kite]
In ΔACD and ΔABD
AC = AB
and
CD = BD [Property of Kite]
AD = AD [Common]
By rule SSS Criteria [Side Side Side ]
ΔACD ≅ ΔABD
∴ ∠CDA = ∠BDA [CPCT]
Now,
In ΔCDE and ΔBDA
CD = BD
∠CDE = ∠BDE
DE = DE [Common]
By rule SAS Criteria [Side Angle Side]
ΔCDE ≅ ΔBDA
∴ CE = BE [CPCT]
Hence, AD bisects BC into equal parts
The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
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