Question

Triangle ABC is reflected across line L to form ΔALBLCL, and AAL intersects line L at point D. Which equation is not necessarily true? A.ALD = BLD B.AD = ALD C.m∠BAC = m∠BLALCL D.m∠ACB = m∠ALCLBL

Answer 1

Answer:

a

Step-by-step explanation:

Answer 2

Answer: Option A i.e. $A_LD=B_LD$ is not necessarily true.

Explanation:

Since, According to the definition of Reflection, If a  shape reflected through any line, then ,we get a congruent shape with respect to given shape.

So, If  $\triangle ABC$ reflected across a line L and makes $\triangle A_LB_LC_L$ then, $\triangle ABC\cong \triangle A_LB_LC_L$

Thus, corresponding measurements must be Congruent.( CPCT )

That is, $AB=A_LB_L$, $AC=A_LC_L$, $BC=B_LC_L$,

$\angle BAC=\angle B_LA_LC_L$, $\angle ABC=\angle A_LB_LC_L$ and $\angle ACB=\angle A_LC_LB_L$

Moreover,The corresponding Distance of vertices from the reflected point D is same for $\triangle ABC$and $\triangle A_LB_LC_L$( according to the property of reflection)

That is, $AD=A_LD$ $BD=B_LD$ and $CD=C_LD$

But, it is not necessary, $AD=B_LD$.

Therefore option first is unnecessary.