AC/AE = BC/DE
DE = 2BC
AE = 2AC
Those are your answers. I( hope this helped!
Answer:
Options B, D, G are the answers.
Step-by-step explanation:
In the figure attached ΔABC and ΔADE are similar.
Now we will check each option given
A). AC = AB
AB = √(2² + 1²) = √5 [ By Pythagoras theorem ]
AC = √(2² + 2²) = √(4 + 4) = √8
Therefore option is not true.
B) [tex]\frac{AC}{AE}=\frac{BC}{DE}[/tex]
In these triangles [tex]tanC=\frac{2}{2}=1[/tex]
∠ C = 45°
and tanE = [tex]\frac{4}{4}=1[/tex]
∠ E = 45°
Similarly ∠B = ∠D
Therefore, by theorem of similar triangles corresponding sides will be in the same ratio.
[tex]\frac{AC}{AE}=\frac{BC}{DE}[/tex]
Option B is true.
C). [tex]\frac{AC}{AD}=\frac{AB}{AE}[/tex]
Since we have proved the ratio of corresponding sides in option B. So this option is not true.
D). DE = 2BC
DE = 4 - (-2) = 4 + 2 = 6 units
BC = 2 - (-1) = 2 + 1 = 3 units
So DE = 6 = 2×3 = 2BC
Therefore, this option is true.
E). BC = 2DE
This option is not correct because DE = 2BE
F). AC = 2AE
AC = √8 = 2√2
AE = √(4² + 4²) = √(16+16)
= √32 = 4√2
Here AC is smaller so this option is not true.
G). AE = 2AC
Since AC = 2√2
and AE = 4√2
Therefore, AE = 2AC
So this option is true.
Finally Options B, D, G are correct.
