Question

The pair of triangles that are congruent by the ASA criterion is . The pair of triangles that are congruent by the SAS criterion is .

Answer 1

The focus of the question is on understanding the criteria for triangle congruence in geometry, namely ASA and SAS, critical for solving high school level geometric problems.

Step-by-step explanation:

The question revolves around the concept of congruent triangles in geometry, specifically highlighting the criteria for establishing congruence between two triangles - ASA (Angle-Side-Angle) and SAS (Side-Angle-Side). The ASA criterion states that two triangles are congruent if two angles and the included side (the side between the two angles) of one triangle are equal to the corresponding parts of another triangle. The SAS criterion specifies that two triangles are congruent if two sides and the included angle (the angle between the two sides) of one triangle are equal to the corresponding parts of another triangle.

Understanding these criteria is crucial to solve geometric problems involving triangle congruence, which is an essential part of high school mathematics curriculums. Examples and step-by-step explanations on how to apply these criteria can help students grasp the concept better and apply them successfully to solve problems.

Answer 2

to be congruent by ASA there must be 2 angles, and the corresponding side (the side connecting the two angles) must be congruent to the same of another triangle

To be congruent by SAS there must be two adjacent sides with the common angle of the two, congruent to these factors of the other triangle