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Could one of this site's math Wizards please help me with this. The teacher wants me to make a 2 column proof that proves this and I am kind of stuck. The topic for this week is triangle inequailities.

 Apr 14, 2019
 #1
avatar+111438 
+1

(1) AB = AC                                      Given

 

(2) Angle ABC = Angle ACB             In a triangle, angles opposite equal sides are also equal

 

(3) Measure of Angle ACB =            Exterior Angle Theorem

Measure of Angle CAD +

Measure of  Angle ADC

 

(4) Measure of Angle ACB >         Consequence of (3)

Measure of Angle ADC

 

(5) Measure of Angle ABC >        Substitution 

Measure of Angle ADC

 

(6) Measure Angle B >                By (5)

Measure Angle D

 

 

cool cool cool

 Apr 14, 2019
edited by CPhill  Apr 14, 2019
 #2
avatar+50 
+1

Thank you for this but I have one question. How is your step 3 the Alternate Exterior Angles Theorem? I do not understand how you got that and I was wondering if you could elaborate.

OkNietzsche  Apr 14, 2019
 #3
avatar+111438 
+1

OK...note that  

 

mAngle ACB  + mAngle  ACD  = 180°     (1)

 

And

 

mAngle CAD + mAngle ADC + mAngle ACD = 180°    (2)

 

So

 

(1) = (2)  so

 

mAngle ACB + mAngle ACD  =  mAngle CAD + mAngle ADC + mAngle ACD

 

Subtract  mACD from each side

 

So

 

mAngle ACB = mAngle CAD + mAngle ADC

 

 

cool cool cool

CPhill  Apr 14, 2019

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