UNIT 5
Congruent Triangles
LESSON 3
Triangle Congruence by ASA and AAS please answers
ASA stands for Angle-Side-Angle. According to the ASA postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
AAS stands for Angle-Angle-Side. According to the AAS theorem, if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
Now, let's apply these concepts to a few examples:
Example 1: Triangle ABC and Triangle DEF are congruent by ASA. Angle A is congruent to Angle D, Angle B is congruent to Angle E, and Side AB is congruent to Side DE. Prove that Triangle ABC is congruent to Triangle DEF.
Solution: Since we are given that Angle A is congruent to Angle D, Angle B is congruent to Angle E, and Side AB is congruent to Side DE, we can conclude that Triangle ABC is congruent to Triangle DEF by the ASA postulate.
Example 2: Triangle XYZ and Triangle WXY are congruent by AAS. Angle Y is congruent to Angle X, Angle Z is congruent to Angle Y, and Side YZ is congruent to Side ZX. Prove that Triangle XYZ is congruent to Triangle WXY.
Solution: Since we are given that Angle Y is congruent to Angle X, Angle Z is congruent to Angle Y, and Side YZ is congruent to Side ZX, we can conclude that Triangle XYZ is congruent to Triangle WXY by the AAS theorem.
Remember, it is important to show all the given congruences in order to apply the ASA or AAS congruence criteria.