Geometry: Triangles

[vampirewitchreine]

(Sorry for the poor quality)

What can you conclude about the length of line AB?
(the measure of angle C is greater than the measure of angle A. line CB= 4)
(the measure of angle B is greater than the measure of angle A. Angle A is congruent to angle C. Line AC=7)

Can someone help me to work out how to do these. I know that I'm using triangle inequalities here, but I need a little help with working out how to do this with angle measures and only one line length given.

I had one that was similar but more information was given:
(the measure of angle C is less than the measure of angle B and the measure of angle B is less than the measure of angle A. line AC=10m line CB=12)

My work for this problem:

AB=x; AC=10; BC=12

AB+AC>BC
x+10>12
x>2

AB+BC>AC
x+12>10
x>-2

AC+BC>AB
10+12>AB
22>AB

Final answer: 2<AB<22

 

[Deleted member 4993]

You'll need to use proposition 18 of Euclid - that states:

A greater side of a triangle is opposite a greater angle.

AB is opposite to angle C and BC is opposite to angle A

You are given: the measure of angle C is greater than the measure of angle A. line CB= 4

So CB < AB → AB > 4

Now try the others...

 

[vampirewitchreine]

Thank you, thank you, thank you, thank you! Everyone on this site are lifesavers. I've used a few other sites before finding this one and no one is anywhere near as good at helping solve the problems or even putting students on the right track to do things themselves. I still have post on these other sites that haven't gotten answers in over a year, and this site I get a reply in no more than a week. I really appreciate everything that y'all do here.