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.

(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)

LunarSF Jan 20, 2021

#1**0 **

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

LunarSF Jan 20, 2021

#2**+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)

MooMooooMooM Jan 20, 2021

#4**+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**0 **

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

#6**+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)

CPhill Jan 20, 2021

#8**+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

CPhill Jan 20, 2021

#9**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.

Melody Jan 20, 2021