Question

PLEASE HELP! 100 points! I only have a few minutes.

In the figure below, ACDF and LA≈ LD. C A F B D E Which additional information would be enough to prove that AABC ADEF? Oa BC EF Ob BCDE Oc AB = DE Od ABBC (By SAS) ​

Answer 1

Answer:

C)  AB ≅ DE

Step-by-step explanation:

According to the Side-Angle-Side (SAS) postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In triangles ABC and DEF, we are given that:

• AC ≅ DF
• ∠A ≅ ∠D

For us to prove that the triangles are congruent by SAS, it is necessary to confirm the congruence of another pair of corresponding sides.

An included angle is the angle formed by two sides at their common vertex. Therefore, angle A is the included angle between sides AC and AB of triangle ABC. Similarly, angle D is the included angle between sides DF and DE of triangle DEF.

Therefore, the additional information that is needed to prove ΔABC ≅ ΔDEF is:

$\LARGE\boxed{\boxed{\overline{AB} \cong \overline{DE}}}$

Answer 2

Answer:

C. $\sf \overline{AB} \cong \overline{DE}$

Step-by-step explanation:

The SAS Axiom, also known as the Side-Angle-Side axiom, is a fundamental principle in Euclidean geometry. It states that , if two triangles have two sides that are equal in length and the included angle between these sides is equal, then the two triangles are congruent.

In this case:

$\sf \overline{AC} \cong \overline{DP}$ Given

$\sf \angle A \cong \angle D$ Given

The remaining additional information, is the side.

So

Here

The side between $\sf \angle A$ and $\angle D$ is $\sf \overline{AB }$ and $\sf \overline{DE}$ respectively.

So, the remaining additional information to prove $\sf \triangle ABC \cong \triangle DEF$ by side-angle-side is:

C. $\sf \overline{AB} \cong \overline{DE}$