A club elects a president vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members
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Consider the given triangles.
Given:
ASA congruence criterion states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
AAS congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Consider the first part:
1. In triangles ABC and QPT
If we take along with the given condition.
Then the triangles are congruent by ASA congruence criterion.
2. If we take and
along with the given condition.
Then the triangles are congruent by ASA congruence criterion.
3. As,,
and
, so the triangles can not be congruent.
4. If we take and
along with the given condition.
Then the triangles are congruent by AAS congruence criterion.
5. If we take AC=TQ=3.2 and CB=QP=3.2 along with the given condition, then the triangles are congruent but by SAS congruence criteria neither by ASA nor AAS congruence criterion.