Question

congruence worksheet #1

1. △abc≅△cda
2. △adc≅△bdc
3. △abe≅△cde
4. △sat≅△sar

Explanation:

Step1: Identify congruence postulates

For $\triangle ABC\cong\triangle CDA$, we have $AD = BC$, $AB=CD$, and $AC = CA$ (common side). By SSS (Side - Side - Side) postulate, the triangles are congruent.

Step2: Analyze $\triangle ADC\cong\triangle BDC$

We have $AC = BC$, $\angle ADC=\angle BDC = 90^{\circ}$, and $CD=CD$ (common side). By SAS (Side - Angle - Side) postulate, the triangles are congruent.

Step3: Examine $\triangle ABE\cong\triangle CDE$

We have $AE = CE$, $BE = DE$, and $\angle AEB=\angle CED$ (vertical angles). By SAS postulate, the triangles are congruent.

Step4: Consider $\triangle SAT\cong\triangle SAR$

We have $SA=SA$ (common side), $\angle SAT=\angle SAR = 90^{\circ}$, and $AT = AR$. By SAS postulate, the triangles are congruent.

Answer:

1. SSS
2. SAS
3. SAS
4. SAS