Question

NEED HELP!!

Answer 1

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) $\frac{AC}{AE}=\frac{BC}{DE}$

In these triangles $tanC=\frac{2}{2}=1$

∠ C = 45°

and tanE = $\frac{4}{4}=1$

∠ E = 45°

Similarly ∠B = ∠D

Therefore, by theorem of similar triangles corresponding sides will be in the same ratio.

$\frac{AC}{AE}=\frac{BC}{DE}$

Option B is true.

C). $\frac{AC}{AD}=\frac{AB}{AE}$

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.

Answer 2

AC/AE = BC/DE

DE = 2BC

AE = 2AC

Those are your answers. I( hope this helped!