Question

What equation is not necessarily true?

Answer 1

The second choice: ALD does not necessarily equal BLD

For ALD to equal BLD would mean that the triangle itself would be isosceles but it never indicated anywhere in the given information that it was isosceles. The first choice is correct because a reflection occurs the same number of units away as the original image, meaning that the distance between the images from the line are equal. The third choice is equal because the triangles are congruent, therefore their angles are congruent, likewise with the fourth choice.
Hope this helps!

Answer 2

Answer:

Option B is not necessarily true.

Step-by-step explanation:

Option A.

AD = $A_{L}D$

Since triangle ABC is reflected to form triangle $A_{L}B_{L}C_{L}$

So distance AD may be equal to distance $A_{L}D$. So this option is true.

Option B.

$A_{L}D$ = $B_{L}D$

This statement is not correct because $A_{L}D$ ≠ $B_{L}D$

Option C.

m∠ACB = m∠$A_{L}C_{L}B_{L}$

Since translated triangle $A_{L}B_{L}C_{L}$ and ΔABC are similar.

So the statement is true.

Option D.

m∠BAC = m∠$B_{L}A_{L}C_{L}$

Since translated triangle $A_{L}B_{L}C_{L}$ and ΔABC are similar.

So the statement is true.

Therefore, option B is not necessarily true.