a Note that the absence of angle markers means there are no congruent angles in that particular triangle.
B
b Note that the absence of side markers means there are no congruent sides in that particular triangle.
C
c Two sides and the included angle of one triangle are congruent to two angles and the included angle of the other triangle. Does this correspond to any congruence theorem?
A
aClassification:
Right triangle.
Obtuse triangle.
Acute triangle.
Equiangular triangle.
B
bClassification:
Equilateral triangle.
Scalene triangle.
Isosceles triangle.
C
c There is enough information.
Proof: See solution.
Practice makes perfect
a Let's classify the triangles one at a time starting with △ 1:
The triangle has a right angle which makes it a right triangle.
The triangle has an obtuse angle which makes it an obtuse triangle.
The triangle has three acute angles and is therefore an acute triangle.
The triangle has three congruent angles and is therefore an equiangular triangle.
b Let's classify the triangles one at a time starting with △ 4:
The triangle has three congruent sides which means this is an equilateral triangle.
The triangle has no congruent sides which means this is a scalene triangle.
The triangle has two congruent sides which means this is an isosceles triangle.
c According to the SAS Congruence Theorem, if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. This is exactly the information we have been given. Therefore, △ 7 ≅ △ 8. Before we can do a proof, we have to label the vertices.
