Answer:
By comparing the ratios of sides in similar triangles ΔABC and ΔADB,we can say that [tex]x^{2} =pz[/tex]
Step-by-step explanation:
Given that ∠ABC=∠ADC, AD=p and DC=q.
Let us take compare Δ ABC and Δ ADB in the attached file , ∠A is common in both triangles
and given ∠ABC=∠ADB=90°
Hence using AA postulate, ΔABC ≈ ΔADB.
Now we will equate respective side ratios in both triangles.
[tex]\frac{AB}{AC}= \frac{AD}{AB}=\frac{BD}{BC}[/tex]
Since we don't know BD , BC let us take first equality and plugin the variables given in respective sides.
[tex]\frac{x}{z}= \frac{p}{x}[/tex]
Cross multiply
[tex]x^{2}=pz[/tex]
Hence proved.
