Triangle Congruency Proofs

$$\angle BCA\cong\angle DCA$$

$$\overline{BC}\cong\overline{DC}$$

$$\angle B\cong\angle D$$

$$\overline{AB}\cong\overline{AD}$$

All right angles are congruent.

Reflexive Property

Definition of Perpendicular Lines

Given

$$ASA\cong$$

$$HL\cong$$

$$SAS\cong$$

$$AAS\cong$$

$$\angle URT\cong\angle SRT$$

$$\overline{UT}\cong\overline{ST}$$

$$\angle U\cong\angle S$$

$$\overline{RU}\cong\overline{RS}$$

Definition of Perpendicular Lines

Reflexive Property

All right angles are congruent.

Given

$$\overline{RU}\cong\overline{RS}$$

$$\angle RTU\cong\angle RTS$$

$$\angle U\cong\angle S$$

$$\overline{RT}\cong\overline{RT}$$

$$\overline{RU}\cong\overline{RS}$$

$$\angle RTU\cong\angle RTS$$

$$\angle U\cong\angle S$$

$$\overline{RT}\cong\overline{RT}$$

$$HL\cong$$

$$SSS\cong$$

$$SAS\cong$$

$$AAS\cong$$