# Congruence and congruent triangles

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##### Intros

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##### Examples

###### Lessons

- Which pairs of triangles are congruent?
- In the following diagram, $\triangle\ GHK$ $\cong$ $\triangle\ QRS$.

i) Find. - The gardener wants to divide a rectangular flower bed into 2 parts as shown in the following figure. Identify if the two parts are the same size and shape.

- Write a two-column proof.

Given: $\overline{AC}$$\cong$$\overline{BD}$, $\overline{AD}$$\cong$$\overline{BC}$, $\angle\ CAD$$\cong$$\angle\ CBD$, $\angle\ ADC$$\cong$$\angle\ BCD$

Prove: $\triangle\ ACD$$\cong$$\triangle\ BDC$- Given: $\overline{XC}$$\cong$$\overline{ZC}$

$\overline{CY}$ bisects $\overline{XZ}$

Prove: $\triangle\ XCY$$\cong$$\triangle\ ZCY$

- Write a flow proof
- Given: $\overline{AC}$$\cong$$\overline{BD}$, $\overline{AD}$$\cong$$\overline{BC}$, $\angle\ CAD$$\cong$$\angle\ CBD$, $\angle\ ADC$$\cong$$\angle\ BCD$

Prove: $\triangle\ ACD$$\cong$$\triangle\ BDC$

- Given: $\overline{XC}$$\cong$$\overline{ZC}$

$\overline{CY}$ bisects $\overline{XZ}$

Prove: $\triangle\ XCY$$\cong$$\triangle\ ZCY$

- Given: $\overline{AC}$$\cong$$\overline{BD}$, $\overline{AD}$$\cong$$\overline{BC}$, $\angle\ CAD$$\cong$$\angle\ CBD$, $\angle\ ADC$$\cong$$\angle\ BCD$