if someone can please do this for me. thank you very much for who does. the lessons are in the attachments.
Given: $\displaystyle \angle B\cong \angle D \ \ and \ \ \angle BCA \cong \angle DCA$.
Prove: $\displaystyle \triangle ABC \cong \triangle ADC$
(1) $\displaystyle \angle B\cong \angle D \ \ and \ \ \angle BCA \cong \angle DCA$. GIVEN
(2) $\displaystyle \overline {AC}=\overline{AC}$ REFLEXIVE PROPERTY OF CONGRUENCE
(3) $\displaystyle \triangle ABC \cong \triangle ADC$ ASA POSTULATE
Given: $\displaystyle \triangle ABC \ \ is \ \ isosceles, \overline{AD} \ \ is \ \ an \ \ altitude$
Prove: $\displaystyle \triangle ADB \cong \triangle ADC$
(1) $\displaystyle \triangle ABC \ \ is \ \ isosceles, \overline{AD} \ \ is \ \ an \ \ altitude$ GIVEN
(2) $\displaystyle \angle B \cong \angle C$ THE BASE ANGLES OF AN ISOSCELES TRIANGLE ARE CONGRUENT
(3) $\displaystyle \overline{AD} \perp \overline{BC}$ DEFINITION OF ALTITUDE OF A TRIANGLE
(4) $\displaystyle \angle ADB \ \ and \ \ \angle ADC$ are right angles. PERPENDICULAR LINES MEET TO FORM RIGHT ANGLES.
(5) $\displaystyle \angle ADB \cong \angle ADC$ ALL RIGHT ANGLES ARE CONGRUENT
(6) $\displaystyle \overline{AD}\cong\overline{AD}$ REFLEXIVE PROPERTY OF CONGRUENCE
(7) $\displaystyle \triangle ADB \cong \triangle ADC$ AAS Theorem