Write a similarity statement relating the three triangles in the diagram.12210107051.jpg

Question

Write a similarity statement relating the three triangles in the diagram.

Answer 1

Step 1

I n △ N O P and △ N Q O

1)

∠ O N P \tilde{=} ∠ Q N O

(same angle)
2)

∠ P O N \tilde{=} O Q N

(right angles)
So,

△ N O P \sim △ N Q O

(by AA property)
Step 2

I n △ N O P and △ O Q P

1)

∠ O P N \tilde{=} ∠ O P Q

(same angle)
2)

∠ P O N \tilde{=} ∠ P Q O

(right angle)
So,

△ N O P \sim △ O Q P

(by AA property)
So,

△ N O P \sim △ O Q P \sim △ N Q O

Result:

△ N O P \sim △ O Q P \sim △ N Q O

.

Expert Answer