Question

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent. What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem? LO ≅ LM OA ≅ MA AngleLOA ≅ AngleLMA AngleLAO ≅ AngleLAM

Answer 1

Answer:

Angle LOA = angle LMA

Step-by-step explanation:

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Answer 2

From the diagram, the two triangles have an indication of a pair of

congruent angles.

• The additional information needed is; ∠LOA ≅ ∠LMA

Reasons:

The given parameters of ΔLOA and ΔLAM are;

The shared side of the triangles = Side LA

From the attached diagram, we have;

∠ALO = ∠ALM

Required:

The additional information needed to prove that the triangles are congruent using AAS

Solution:

The AAS congruency is an acronym for Angle Angle Side, which states

that, two triangles are similar if two angles and a non included side of one

triangle are equal to two angles and a non included side on another

triangle, then the two triangles are congruent.

The angle on ΔLOA that will make the side LA a non included side is ∠LOA.

Similarly;

The angle on ΔLAM that will make the side LA a non included side is ∠LMA.

Therefore, the additional information needed to prove that the triangle are congruent using the AAS congruency theorem is; ∠LOA ≅ ∠LMA

Learn more about Angle Angle Side, AAS, rule of congruency here:

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