b Two pairs of legs and the included angle are congruent.
C
c The triangles share an angle at J.
D
d Two triangles are congruent if they have the same shape and size.
A
aCongruence Statement: △ CAB ≅ △ CED
Congruence Condition: ASA Congruence Theorem
B
bCongruence Statement: △ CBD ≅ △ EFG
Congruence Condition: SAS Congruence Theorem
C
cCongruence Statement: △ LJI ≅ △ HJK
Congruence Condition: SAS Congruence Theorem
D
dCongruent? Can't claim congruence.
Explanation: See solution.
Practice makes perfect
a Examining the diagram, we see that the triangles have a pair of congruent angles as well as a pair of congruent sides. We can also identify two angles that form a pair of vertical angles.
Since two pairs of angles and their included side are congruent, we can claim that the triangles are congruent by the ASA (Angle-Side-Angle) Congruence Theorem.
△ CAB ≅ △ CED
b Examining the diagram, we notice that two pairs of legs and their included angle are congruent in the triangles. Therefore, we can claim congruence by the SAS (Side-Angle-Side) Congruence Theorem.
△ CBD ≅ △ EFG
c Examining the diagram, we see that â–³ LJI and â–³ HJK share the angle at J. Let's add this information to the diagram.
If we separate the triangles, it is easier to see if they are congruent.
Now we notice that two pairs of sides and their included angle in the triangles are congruent. Therefore, we can claim congruence by the SAS Congruence Theorem.
△ LJI ≅ △ HJK
d Notice that the two triangles have three pairs of congruent angles. Therefore, we know the triangles are similar by the AA (Angle-Angle) Similarity Theorem. However, to claim congruence we also have to be able to claim that one pair of corresponding sides is congruent. We do not have this information, so we cannot claim congruence.
