Question

2 - 45. a laser light is pointed at a mirror as shown at right. if ∠s measures 46°, what are the measures of ∠y and ∠z? justify your reasons. homework help 2 - 46. are the triangles below similar? if so, write a flowchart proof that justifies your conclusion. if not, explain how you know. homework help

Explanation:

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Step1: Use the law of reflection

The angle of incidence is equal to the angle of reflection. If $\angle s = 46^{\circ}$, then $\angle z=\angle s = 46^{\circ}$ because of the law of reflection of light.

Step2: Find $\angle y$

The normal to the mirror and the mirror surface are perpendicular. The sum of $\angle s$ and $\angle y$ is $90^{\circ}$ since the normal to the mirror forms a right - angle with the mirror. So, $\angle y=90^{\circ}-\angle s$. Substituting $\angle s = 46^{\circ}$, we get $\angle y = 90^{\circ}-46^{\circ}=44^{\circ}$.

Step1: Check for similar - triangle criteria

In $\triangle ABC$ and $\triangle DEC$, $\angle ABC=\angle DEC = 90^{\circ}$ (right - angles). Also, $\angle C$ is common to both triangles.

Step2: Apply AA (angle - angle) similarity criterion

Since two angles of $\triangle ABC$ are equal to two angles of $\triangle DEC$ (the right - angles and the common angle $\angle C$), by the AA similarity criterion, $\triangle ABC\sim\triangle DEC$.

Answer:

$\angle y = 44^{\circ}$, $\angle z = 46^{\circ}$

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