Question

1. an artist is designing a logo for a new company by reflecting triangle abc across a vertical line to produce triangle def. find each measure. measure of ∠d: ____. length of ef: __ in. length of df: ____ in.

Explanation:

Step1: Recall reflection property

When a figure is reflected, corresponding angles are congruent. So $\angle D=\angle A$. Given $\angle A = 58^{\circ}$, then $\angle D=58^{\circ}$.

Step2: Recall reflection property for side - lengths

When a figure is reflected, corresponding side - lengths are equal. Side $EF$ corresponds to side $BC$. So $EF = BC=3.5$ inches.

Step3: Recall reflection property for side - lengths

Side $DF$ corresponds to side $AC$. So $DF = AC = 4$ inches.

Answer:

measure of $\angle D$: $58^{\circ}$
length of $EF$: $3.5$ in.
length of $DF$: $4$ in.