Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
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Exercise 1 Page 651

We already know the following is true.
We also have to show that the included angles, and are congruent as well.

Angles

If we look at the diagram, we see that and are vertical angles. According to the Vertical Angles Congruence Theorem, vertical angles are congruent.

Conclusion

Since we now know that two sides and the included angle of are congruent to two sides and the included angle of , we can claim by the SAS Congruence Theorem that the triangles are congruent.

Proof

Two-Column Proof

Let's also show this as a two-column proof.

Statement Reason
Given
Vertical Angles Congruence Theorem
SAS Congruence Theorem