Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
7. Using Congruent Triangles
Continue to next subchapter

Exercise 23 Page 638

What do you know about â–ł ABC and how does that limit the theorems we can use to prove congruence?

â–ł GHJ and â–ł NPQ

Practice makes perfect

Examining â–ł ABC, we notice a couple of things.

  1. Two angles are marked, one of them a right angle.
  2. Both legs are marked.
Given the information, we can limit the theorems that can be used to prove congruence to the following three.

&SAS Congruence Theorem &ASA Congruence Theorem &AAS Congruence Theorem

SAS

To use SAS, we need to know two sides and the included angle in any of the triangles. If they are congruent to two sides and the included angle of â–ł ABC, we can prove congruence by the SAS Congruence Theorem.

ASA and AAS

To use either of these theorems, we need two angles and the included side (ASA) or non-included side (AAS) of any of the triangles. If they are congruent to two angles and the included or non-included side of â–ł ABC, we can prove congruence by the ASA Congruence Theorem or the AAS Congruence Theorem.

Conclusion

The only triangles that fit either of these descriptions are â–ł GHJ and â–ł NPQ.