Final answer:
In a kite with given side lengths, the measures of segments EB, AB, and BC can be found using the congruent triangles formed. EB = 10 - x, AB = 10 + x, and BC = 18 + x, where x is the length of segment DE.
Step-by-step explanation:
A kite is a quadrilateral with two sets of adjacent sides that are congruent. In the given problem, quadrilateral ABCD is a kite. AD = 10, DB = 24, and DC = 18.
We need to find the measures of segments EB, AB, and BC.
Since AD and DC are congruent, we know that angle DAC is congruent to angle ACD.
This means that triangle ADE is an isosceles triangle.
By the Isosceles Triangle Theorem, we can conclude that angle AED is congruent to angle EAD. Therefore, triangle ADE is congruent to triangle EAD.
Now, let's use the information given to find the lengths of the segments EB, AB, and BC using the congruent triangles:
- EB = AD - DE = 10 - x, where x is the length of segment DE
- AB = AD + DE = 10 + x
- BC = DC + DE = 18 + x