Given that ∠Abc ≅ ∠Dbe, we can conclude that the statement ∠Cbd ≅ ∠Abc must be true. This can be deduced using the transitive property of congruence.

The transitive property states that if two angles are congruent to the same angle, then they are congruent to each other. In this case, since ∠Abc ≅ ∠Dbe and ∠Dbe ≅ ∠Cbd, we can use the transitive property to determine that ∠Abc ≅ ∠Cbd.

Now, let’s take a look at some common questions related to this statement:

1. What is the given information?

The given information is that ∠Abc ≅ ∠Dbe.

2. What does ≅ represent?

≅ represents congruence, meaning that the two angles are equal in measure.

3. What does ∠Abc refer to?

∠Abc refers to angle ABC.

4. What does ∠Dbe refer to?

∠Dbe refers to angle DBE.

5. What is the statement that must be true based on the information given?

The statement that must be true is ∠Cbd ≅ ∠Abc.

6. Can we conclude that ∠Abd ≅ ∠Cbe?

No, we cannot conclude that ∠Abd ≅ ∠Cbe based on the given information.

7. What is the transitive property of congruence?

The transitive property states that if two angles are congruent to the same angle, then they are congruent to each other.

8. How can we prove that ∠Cbd ≅ ∠Abc using the transitive property?

We can use the transitive property by combining the given information: ∠Abc ≅ ∠Dbe and ∠Dbe ≅ ∠Cbd.

9. What does it mean for two angles to be congruent?

Two angles are congruent if they have the same measure.

10. Can we conclude that ∠Cbd ≅ ∠Cbe?

No, we cannot conclude that ∠Cbd ≅ ∠Cbe based on the given information.

11. Can we conclude that ∠Cbd + ∠Dbe = ∠Abc + ∠Abd?

No, we cannot conclude that ∠Cbd + ∠Dbe = ∠Abc + ∠Abd based on the given information.

12. What other properties of congruence can we use to determine angle congruence?

Other properties of congruence include the reflexive property, symmetric property, and angle addition postulate. However, these properties are not applicable to the given scenario.