Question

problem 13: (first taught in lesson 32) given △bcd ≅ △cbe in the diagram, fill in each of the blanks. after you enter your answer press go. bc ≅ be ≅ ∠dbc ≅ ∠

Explanation:

Step1: Reflexive property for $\overline{BC}$

In congruent triangles, a side is congruent to itself. So $\overline{BC}\cong\overline{CB}$.

Step2: Corresponding - parts of congruent triangles

Since $\triangle BCD\cong\triangle CBE$, corresponding sides are congruent. $\overline{BE}$ and $\overline{CD}$ are corresponding sides, so $\overline{BE}\cong\overline{CD}$.

Step3: Corresponding - parts of congruent triangles

Since $\triangle BCD\cong\triangle CBE$, corresponding angles are congruent. $\angle DBC$ and $\angle ECB$ are corresponding angles, so $\angle DBC\cong\angle ECB$.

Answer:

1. $\overline{BC}\cong\overline{CB}$
2. $\overline{BE}\cong\overline{CD}$
3. $\angle DBC\cong\angle ECB$