# Which side is longer? And why please?!

#### Subhotosh Khan

##### Super Moderator
Staff member
AB and BC are shorter than AD and DC.

Why? - you prove it!

Hint:

There is a theorem in geometry that states:

In a triangle, the side contending the larger angle is longer in length.

##### New member
Yes thank you. However what about AC?

#### Subhotosh Khan

##### Super Moderator
Staff member
Yes thank you. However what about AC?
It is still your turn - look at the diagram carefully and what do you observe?

##### New member
I have no idea - I’m sorry. Which is why I’m asking for help.

#### Subhotosh Khan

##### Super Moderator
Staff member
Play with the drawing and the given theorem!

#### Dr.Peterson

##### Elite Member
Yes thank you. However what about AC?
Look at triangle ABC. What are the base angles?

#### pka

##### Elite Member
I have no idea - I’m sorry. Which is why I’m asking for help.
$$\displaystyle m(\angle DAC)=61^o$$ please tell us why that is the case.

##### New member
Triangle DAC has base angles of 61 because the 3 angles add up to 360 degrees and the base angles are the same .
Triangle ABC has base angles of 59 degrees for the same reason

#### Dr.Peterson

##### Elite Member
Do you see that this leads to the conclusion you want, by the theorem stated in post #2?

##### New member
No. I don’t see.

What do you mean the side with the larger angle is longer. This doesn’t make sense.

#### Subhotosh Khan

##### Super Moderator
Staff member
No. I don’t see.

What do you mean the side with the larger angle is longer. This doesn’t make sense.
It is not "with" - it is "subtending": .....................edited

the side subtending the larger angle is longer. .....................edited

A translation of that could be:

the side (in a triangle) "opposite to" the larger angle is longer.

Have you taken any formal geometry? This is one of the early theorems!

#### Jomo

##### Elite Member
Draw a line through point B that meets line AC at a right angle. Make sure this line you drew goes above point B as well.
Now pick a point W on this line (or several points) below B and draw a line from W to A and other from W to point C. Is the angle at point W smaller or larger than angle B? Now pick a point on the line you drew above point B. Call this point V. Is angle V more or less than angle B? Do you get my drift?