Exercise 8 Page 647

Are the congruent angles included?

There is not enough information.

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For the SAS Congruence Theorem, we need two corresponding sides and the included angle from each triangle to be congruent. In addition to what the diagram tells us, we can by the Reflexive Property of Congruence identify a second pair of congruent sides in our triangles, XZ.

In this case, the congruent angles are not included by the congruent sides. Thus, there is insufficient information to use the SAS Congruence Theorem.

Subchapter links

1 Angles of Triangles p.646

2 Congruent Polygons p.646

3 Proving Triangle Congruence by SAS p.647

4 Equilateral and Isosceles Triangles p.647

5 Proving Triangle Congruence by SSS p.648

6 Proving Triangle Congruence by ASA and AAS p.649

7 Using Congruent Triangles p.649

8 Coordinate Proofs p.650

Exercise 8 Page 647

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