Question

you can construct a periscope with two parallel mirrors, as shown in the diagram. a ray of light enters from the object. it reflects off the first mirror and then the second mirror to the eye. use the diagram to answer the question. what can you conclude about ∠1 and ∠4? what property enables you to make that deduction? click the icon to view the law of reflection. you can use the law of reflection and theorems about the angles formed when parallel lines are cut by a transversal to show that ∠1 and ∠2 are and ∠3 and ∠4 are that ∠2 and ∠3 are

Explanation:

Step1: Recall the Law of Reflection

The angle of incidence equals the angle of reflection. For the first - mirror, if the angle of incidence of the light ray is related to ∠1 and for the second - mirror, the angle of incidence is related to ∠4.

Step2: Consider parallel mirrors

Since the two mirrors are parallel, the normal lines to the mirrors are also parallel. The light - ray path forms a set of parallel - lines and transversals situation. By the Law of Reflection, ∠1 and ∠2 are equal (angle of incidence equals angle of reflection for the first mirror), ∠3 and ∠4 are equal (angle of incidence equals angle of reflection for the second mirror), and also ∠2 and ∠3 are equal (alternate interior angles for parallel lines).

Step3: Transitive property

Since ∠1 = ∠2, ∠2 = ∠3, and ∠3 = ∠4, by the transitive property of equality, ∠1=∠4.

Answer:

∠1 = ∠4; the transitive property of equality and the Law of Reflection along with properties of angles formed by parallel lines and transversals enable this deduction. ∠1 and ∠2 are equal (by the Law of Reflection), ∠2 and ∠3 are equal (alternate interior angles for parallel mirrors' normal lines), and ∠3 and ∠4 are equal (by the Law of Reflection).