Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
Chapter Test
Continue to next subchapter

Exercise 1 Page 651

What can we say about ∠ ACB and ∠ ECD?

See solution.

Practice makes perfect
We already know the following is true. CA ≅ CB≅ CD ≅ CE

We also have to show that the included angles, ∠ ACB and ∠ DCE are congruent as well.

Angles

If we look at the diagram, we see that ∠ ACB and ∠ ECD 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 △ ABC are congruent to two sides and the included angle of △ EDC, 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
1.
CA ≅ CB≅ CD ≅ CE
1.
Given
2.
∠ ACB ≅ ∠ ECD
2.
Vertical Angles Congruence Theorem
3.
△ ABC ≅ △ EDC
3.
SAS Congruence Theorem