McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
3. Proving Triangles Congruent-SSS, SAS
Continue to next subchapter

Exercise 18 Page 359

Look at the position of the angle that is marked on the figure.

Not possible.

Practice makes perfect
Let's check if we can use either the Side-Side-Side (SSS) or the Side-Angle-Side (SAS) postulate.
  • To use the Side-Side-Side Congruence Postulate, we need three pairs of congruent sides. On the figure the markers only indicate two pairs of congruent sides. The SSS postulate does not guarantee that these triangles are congruent.
  • To use the Side-Angle-Side Congruence Postulate we need congruent angles included between the congruent sides. On the figure, the markers indicate that the congruent angles are not included between the marked congruent sides. The SAS postulate does not guarantee that these triangles are congruent.

Therefore, by using the SSS or SAS postulates it is not possible to determine whether the two triangles are congruent.

Extra

Why we cannot use Side-Side-Angle (SSA)

The relationship given in the exercise is often called Side-Side-Angle(SSA). As a general rule, we cannot use SSA to prove triangle congruence. If given the measurements of the triangle, without proper context, there are two possible lengths for the third side. We can draw an example of this situation.