# help with these two triangle lessons.

• Nov 17th 2008, 12:19 PM
dgenerationx2
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.
• Nov 17th 2008, 01:22 PM
masters
Quote:

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: $\displaystyle \angle B\cong \angle D \ \ and \ \ \angle BCA \cong \angle DCA$.

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