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8-44.
  1. If the triangles in each diagram below are congruent, state which triangle congruence condition can be used. If the triangles are not congruent or if there is not enough information, state, “Cannot be determined”. Then calculate the value of x in each diagram, if possible. Homework Help ✎

  2. a.

    b.

    c.

    d.

Read the Math Notes box in Lesson 7.1.7 on the triangle congruence conjectures.
Are the two triangles in each part congruent?

To prove the triangles congruent notice both triangles have a side that is 7.
Also, use alternate interior angles with the 73° angle.
Finally both triangles share the diagonal so based on the reflexive property these sides are congruent.
Finally the triangles are congruent by SAS congruence.
So using the triangle sum theorem, x = 79°.

Cannot be determined, because the triangles cannot be found to be congruent.
If the 23° angle was between the 6 and the 9 on both triangles
then the triangles would be congruent by ASA. Since they are not then the triangles are not congruent.