Question

In the given figure, m and n are two plane
mirrors perpendicular to each other. Show
that the incident ray CA is parallel to the
reflected ray BD.
2
Α.​

Answer 1

dear you forget to attach the figure.

Answer 2

Answer:

Step-by-step explanation:

Solution:

Construct a line m and n from A and B intersect at P

So we get

OB ⊥ m and OC ⊥ n

So m ⊥ n

We can also write it as

OB ⊥ OC

Since APB is a right angle triangle

We know that ∠APB = 90

So we can write it as

∠APB = ∠PAB + ∠PBA

By substituting the values

90 = ∠2 + ∠3

We know that angle of incidence is equal to the angle of reflection

So we get

∠1 = ∠2 and ∠4 = ∠3

It can be written as

∠1 + ∠4 = ∠2 + ∠3 = 90

We can write it as

∠1 + ∠2 + ∠3 + ∠4 = 180

We know that ∠1 + ∠2 = ∠CAB and ∠3 + ∠4 = ∠ABD

∠CAB + ∠ABD = 180

According to the diagram ∠CAB and ∠ABD are consecutive interior angles when the transversal AB cuts BD and CA.

Therefore, it is proved that CA || BD.