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

d

Step-by-step explanation:

Answer 2

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

Step-by-step 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.