Question

Using SAS Congruence Theorem, fill in the blanks with what is needed to prove that Triangle ABC ≅ Triangle OMG:

A) Angle B is congruent to Angle M
B) Angle A is congruent to Angle O
C) Line Segment AC is congruence to Line Segment OG
D) Line Segment AB is congruence to Line Segment OM

Answer 1

To prove Triangle ABC congruent to Triangle OMG using the SAS Congruence Theorem, we must show two pairs of sides and one pair of angles are congruent, specifically Angle B ≅ Angle M, Line Segment AC ≅ Line Segment OG, and Line Segment AB ≅ Line Segment OM.

Step-by-step explanation:

In order to prove that Triangle ABC is congruent to Triangle OMG using the SAS Congruence Theorem, we need to identify two pairs of corresponding sides that are congruent and one pair of corresponding angles that are congruent. The theorem states that if two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.

Given the information:

• Angle B is congruent to Angle M (Angle B ≅ Angle M)
• Line Segment AC ≅ Line Segment OG

We can complete the requirements for SAS by proving the third piece of information needed:

• Line Segment AB ≅ Line Segment OM