Answer :
Answer:
A) ZA = 3 cm
Step-by-step explanation:
The triangle is shown below.
From the triangle, A is the concurrency point of angle bisectors of all vertices.
Consider ΔAYD,
Using Pythagorean theorem,
[tex]AD^2=AY^2+ YD^2\\5^2=AY^2+4^2\\25=AY^2+16\\AY^2=25-16\\AY=\sqrt{9}=3[/tex]
Consider triangles ADY and ADZ.
[tex]\angle AYD\cong \angle AZD=90\\\angle ADY\cong \angle ADZ \textrm{ (angle bisector) }\\AD\cong AD\textrm{ (Common side)}[/tex]
The two triangle are congruent by AAS postulate.
Therefore, by CPCTE, [tex]AY=ZA=3\textrm{ cm}[/tex]
