The unknown leg is 6 units. Since the two triangles have three pairs of congruent corresponding sides, we know that they are congruent by the SSS Congruence condition.
b From the diagram, we notice that the triangles have two pairs of congruent angles. This means we can claim similarity by the AA Similarity condition. To determine if the triangles are congruent, we have to identify corresponding sides.
Since one pair of corresponding sides are congruent, we can claim congruence by the AAS Congruence condition.
c Examining the diagram, we notice one pair of congruent angles and one pair of congruent sides. Upon further inspection, we see that the two triangles also share a side. By the Reflexive Property of Congruence, we know that this side is congruent as well.
However, there is no corresponding congruence condition. Therefore, we cannot prove congruence.
d Like in Part C, we have two triangles where one pair of sides and one pair of angles are already marked as congruent. Also, the two triangles share a side, which means this side is congruent by the Reflexive Property of Congruence.
With this information, we can claim congruence using the SAS Congruence condition.
Flowchart
If we want to show the proof as a flowchart we have to label the vertices of the diagram.
