help with these two triangle lessons.

**dgenerationx2** · November 17th 2008, 12:19 PM

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

**masters** · November 17th 2008, 01:22 PM

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

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