# Thread: help with these two triangle lessons.

1. ## help with these two triangle lessons.

if someone can please do this for me. thank you very much for who does. the lessons are in the attachments.

2. Originally Posted by dgenerationx2
if someone can please do this for me. thank you very much for who does. the lessons are in the attachments.
Given: $\angle B\cong \angle D \ \ and \ \ \angle BCA \cong \angle DCA$.

Prove: $\triangle ABC \cong \triangle ADC$

(1) $\angle B\cong \angle D \ \ and \ \ \angle BCA \cong \angle DCA$. GIVEN

(2) $\overline {AC}=\overline{AC}$ REFLEXIVE PROPERTY OF CONGRUENCE

(3) $\triangle ABC \cong \triangle ADC$ ASA POSTULATE

Given: $\triangle ABC \ \ is \ \ isosceles, \overline{AD} \ \ is \ \ an \ \ altitude$

Prove: $\triangle ADB \cong \triangle ADC$

(1) $\triangle ABC \ \ is \ \ isosceles, \overline{AD} \ \ is \ \ an \ \ altitude$ GIVEN

(2) $\angle B \cong \angle C$ THE BASE ANGLES OF AN ISOSCELES TRIANGLE ARE CONGRUENT

(3) $\overline{AD} \perp \overline{BC}$ DEFINITION OF ALTITUDE OF A TRIANGLE

(4) $\angle ADB \ \ and \ \ \angle ADC$ are right angles. PERPENDICULAR LINES MEET TO FORM RIGHT ANGLES.

(5) $\angle ADB \cong \angle ADC$ ALL RIGHT ANGLES ARE CONGRUENT

(6) $\overline{AD}\cong\overline{AD}$ REFLEXIVE PROPERTY OF CONGRUENCE

(7) $\triangle ADB \cong \triangle ADC$ AAS Theorem