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I know I'm not supposed to have help for homework problems but I'm really stuck on these 3, if possible can you please help and explain? Much appreciated. laugh

 

(A) The figure below is not drawn to scale. We are given the angle measures in the figure below. Which of AB, AC, AD, BC, BD, and CD is the shortest side.

(B) The figure below is not drawn scale. We are given that ∠ADB is obtuse.

      Which of the following statements must be true? (Scroll down and select A, B, C, or D)

      i. BD < AB

      ii. CD < AB

A: (i) only
B: (ii) only
C: (i) and (ii)
D: neither (i) nor (ii)

 

(C)The figure below is not drawn to scale. We are given that ∠ADB is obtuse and that AD bisects ∠BAC.

     Which of the following statements must be true? (Scroll down and select A, B, C, or D)

      i. AD < BC

      ii. CD < AB

A: (i) only
B: (ii) only
C: (i) and (ii)
D: neither (i) nor (ii)

 Jan 20, 2021
 #1
avatar+15 
0

Also I'm a new user, so please tell me if these images work or not ... many thanks!

 Jan 20, 2021
 #2
avatar+536 
+1

I can start on the first question...

The shortest side would be the one across from the smallest angle since the larger the angle, the opposite side gets bigger in comparison to the others. (just look at a right triangle)

 Jan 20, 2021
 #3
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0

That does make sense ... but what if another angle in the triangle makes the opposite line tilt in such a way that it is no longer that short? Can you explain a little bit more? smileyI'm still kind of confused ... 

LunarSF  Jan 20, 2021
edited by LunarSF  Jan 20, 2021
edited by LunarSF  Jan 20, 2021
 #4
avatar+536 
+1

I mean i dont know much about it myself since geo is my worst subject

But It should be that the smallest side of a triangle is opposite to the smallest angle in a triangle

MooMooooMooM  Jan 20, 2021
 #5
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Thank you for your help anyways, can you judge if this is correct? -

I did some calculations and got CD, not sure if I'm right, may someone please check this answer? I just compared all the lengths to AD after figuring out it's side length, is this the right way to go?

As for the third one I know ii is true but I'm not sure about i ... 

LunarSF  Jan 20, 2021
edited by LunarSF  Jan 20, 2021
edited by LunarSF  Jan 20, 2021
 #6
avatar+116125 
+2

First one 

 

Angle ADC  = 180 - 120  =  60°

 

So angle CAD  = 180 - 60  - 65  =  55°

 

The  length of the sides   are   in line with  their opposite angles

Greatest angle  opp  greatest side

Next greatest angle opp next greatest  side

Least angle opp  shortest side

 

So

 

AD >  AC >  CD    (1)

 

And note that  angle ADB   =  180  -  120  - 35     = 25°

 

So   AB > BD  > AD     (2)

 

So   (1) and (2) imply that

 

AB > BD > AD > AC  >  CD

 

So  CD  is the  shortest side       (clearly, BC  is greater than CD)

 

cool cool cool

 Jan 20, 2021
 #7
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Thanks for explaining. It really helped. laugh 

LunarSF  Jan 20, 2021
edited by LunarSF  Jan 20, 2021
 #8
avatar+116125 
+2

(B)  

 

Since angle ADB  is obtuse....it is the greatest angle in triangle ADB

So BD <  AB

 

We can't say anything about the  relationship between CD and AB....we  would have to  know something about the ,measures of angles CAD  and DAB

 

 

For instance   angle   ADB  is obtuse   so   BD  <  AB

 

But here   CD is clearly >  AB

 

cool cool cool

 Jan 20, 2021
 #9
avatar+112523 
0

Next time please post only one question at a time.

 

If I had seen it before the other answerers this question would have been deleted.

But it appears that you tried to learn from their answers so it is probably just as well they saw it before me.  

 

Next time, just one question though.

 Jan 20, 2021
edited by Melody  Jan 20, 2021
edited by Melody  Jan 20, 2021
 #10
avatar+15 
+1

Sorry ... I didn't realize.

LunarSF  Jan 22, 2021

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