Question

given: (overline{dc}congoverline{bc}) and (angle dcacongangle bca) prove: (angle dcongangle b) arrange the cards to complete the proof. fill in the blank where indicated. mark all of congruent sides and angles if the corresponding congruence statement is justified in the proof.

Explanation:

Step1: State the first given

$\overline{DC}\cong\overline{BC}$ (Given)

Step2: State the second given

$\angle DCA\cong\angle BCA$ (Given)

Step3: State the reflexive property

$\overline{AC}\cong\overline{AC}$ (Reflexive Property)

Step4: Prove triangles congruent

$\triangle DAC\cong\triangle BAC$ (By SAS - Side - Angle - Side congruence, since we have two sides and the included angle congruent: $\overline{DC}\cong\overline{BC}$, $\angle DCA\cong\angle BCA$, $\overline{AC}\cong\overline{AC}$)

Step5: Use CPCTC

$\angle D\cong\angle B$ (CPCTC - Corresponding Parts of Congruent Triangles are Congruent)

Answer:

1. $\overline{DC}\cong\overline{BC}$ (Given)
2. $\angle DCA\cong\angle BCA$ (Given)
3. $\overline{AC}\cong\overline{AC}$ (Reflexive Property)
4. $\triangle DAC\cong\triangle BAC$ (SAS)
5. $\angle D\cong\angle B$ (CPCTC)