We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
52
3
avatar+45 


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+100571 
+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+45 
+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+100571 
+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

18 Online Users

avatar
avatar
avatar
avatar
avatar