# More Triangles

• Apr 30th 2007, 05:58 PM
whytechocolate01
More Triangles

Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.

Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB

To Prove: Line CD bisects Angle ACB

Plan: __________________________

Proof:

Statements: ___________________

Reasons: ______________________
• Apr 30th 2007, 07:27 PM
CaptainBlack
Quote:

Originally Posted by whytechocolate01

Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.

Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB

To Prove: Line CD bisects Angle ACB

Plan: __________________________

Proof:

Statements: ___________________

Reasons: ______________________

In the isosceles triangle ABC, we assume that it is sides AC and BC that
are equal.

angle CDA = angle CDB and both are right angles, as CD is an altitude
from AB to C.

angle CAD = angle CBD as they are the angles opposite the equal sides
of an isosceles triangle.

angle ACD = angle DCB as these are the third angles in two triangles whose
other two angle are equal and so equal because the angle sum of any
triangle is two right angles.

Therefore as side CD is common to both triangle ACD and triangle BCD
these triangles are congruent by ASA.

Hence AD is congruent to DC as these are corresponding sides of congruent
triangles. So we have proven that D bisects AC.

RonL
• May 1st 2007, 05:58 AM
whytechocolate01
:( Still confused...
Uhm...i'm still confused. Which are the statements and reasons? And why? How did you get to that? I'm sorry math is not my strongest point but this is a really important assignment. Please be patient with me. I'm sorry for the trouble. :( But i'm so confused. Please explain more thoroughly if it's not too much trouble. Thank you.
• May 1st 2007, 12:43 PM
Quick
Quote:

Originally Posted by whytechocolate01

Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.

Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB

To Prove: Line CD bisects Angle ACB

Plan: Prove that angle ACD is congruent to angle BCD

1. ADC and BDC are triangles
2. CDA and CDB are right angles (altitudes make right angles)
3. CAD and CBD are congruent (It's an isosceles triangle)
4. 180 - CDA - CAD = ACD (angles in a triangle add to 180)
5. 180 - CDB - CBD = BCD (angles in a triangle add to 180)
6. 180 - CDA -CAD = BCD (substitution)
7. ACD = BCD (Transitive property)
8. ACD and BCD are congruent
9. CD bisects ACB (A line separating two equal angles is a bisector)