Answer :
Answer:
Δ ABC is similar to Δ EDF and [tex]x = r\frac{w}{z}[/tex]
Step-by-step explanation:
In Δ ABC, ∠ A = 47° and ∠ C = 62°
So, ∠ B = 180° - 62° - 47° = 71°
Again, in Δ EDF, ∠ D = 71°, and ∠ E = 47°
So, ∠ F = 180° - 71° - 47° = 62°
Hence, Δ ABC is similar to Δ EDF
Now, for two similar triangles the ratio of corresponding sides will be in the same ratio.
So, [tex]\frac{BC}{DF} = \frac{AB}{ED}[/tex]
⇒ [tex]\frac{x}{r} = \frac{w}{z}[/tex]
⇒ [tex]x = r\frac{w}{z}[/tex].
Therefore, the correct option is 3. (Answer)
Answer:
[tex]\triangle ABC \sim \triangle ED\ F\\[/tex]
[tex]x=r \times \frac{w}{z}[/tex]
Step-by-step explanation:
The given triangles are similar by Angle-Angle postulate, because all three pairs of corresponding angles are congruent.
Triangle ABC
[tex]\angle A + \angle B + \angle C = 180\°\\47\° + \angle B + 62\° = 180\°\\\angle B = 180\° - 62\° - 47\°= 71\°[/tex]
Triangle DEF
[tex]\angle D + \angle E + \angle F = 180\°\\71\° + 47\° + \angle F = 180\°\\\angle F = 180\° - 71\° - 47\°=62\°[/tex]
As you can see,
[tex]\angle A = \angle E\\\angle B = \angle D\\\angle C = \angle F[/tex]
Therefore, triangles are similar, that is
[tex]\triangle ABC \sim \triangle ED\ F[/tex]
From the similarity, we deduct the following proportions
[tex]\frac{AB}{ED}=\frac{BC}{DF}=\frac{AC}{EF}[/tex]
According to the problem, [tex]x = BC; y= AC;w=AB\\r = DF; u=EF; z=De[/tex]
From proportions, we have
[tex]\frac{BC}{DF}=\frac{AB}{ED}\\\frac{x}{r}=\frac{w}{z}\\ x=r \times \frac{w}{z}[/tex]
Therefore, the right answer is the last choice.