# Congruence and congruent triangles

0/1
##### Introduction
###### Lessons
1. Similar tirangles VS. Congruent triangles
2. Ways to prove congruency:
• SSS
• SAS
• ASA
• AAS
0/13
##### Examples
###### Lessons
1. Which pairs of triangles are congruent?

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$

###### Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
• #### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.