# Congruence and congruent triangles #### Everything You Need in One Place

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###### Lessons
1. Similar tirangles VS. Congruent triangles
2. Ways to prove congruency:
• SSS
• SAS
• ASA
• AAS
##### Examples
###### Lessons
1. Which pairs of triangles are congruent?

1. 2. 3. 2. In the following diagram, $\triangle\ GHK$ $\cong$ $\triangle\ QRS$. i) Find.
1. m$\angle\ G$ = ?
2. m$\angle\ R$ = ?
3. SR = ?
4. $\overline{HK}$ = ?
5. Find m$\angle\ R$.
3. 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. 1. Write a two-column proof.

1. 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$
2. Given: $\overline{XC}$$\cong$$\overline{ZC}$
$\overline{CY}$ bisects $\overline{XZ}$
Prove: $\triangle\ XCY$$\cong$$\triangle\ ZCY$ 2. Write a flow proof
1. 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$ 2. Given: $\overline{XC}$$\cong$$\overline{ZC}$
$\overline{CY}$ bisects $\overline{XZ}$
Prove: $\triangle\ XCY$$\cong$$\triangle\ ZCY$ 