Geometry Question (1 Viewer)

[Arucerious]

 

[kawaiipotato]

b) Draw a parallel line, parallel to both EF and CB through C.
The angle 'Y' will split up into two angles. Using your alternate angles (parallel lines), then the two angles are alpha and beta, which add up to angle 'Y'
Hence Y = alpha + beta
d) The converse of (b). Split up angle ADE into two by drawing a line (make it parallel to only ONE line, either AB or EF) through D. Make it parallel to, for example, AB. Using alternate angles, then one of the angle in ADE will be equal to alpha. Hence, the other angle must be beta. But angle DEF = beta. Therefore EF is parallel to line through D (alternate angles equal) which means it's parallel to AB

 

[Drsoccerball]

Draw a parallel line through c and use the property "Co interior angles are supplementary"

 

[Arucerious]

b) Draw a parallel line, parallel to both EF and CB through C.
The angle 'Y' will split up into two angles. Using your alternate angles (parallel lines), then the two angles are alpha and beta, which add up to angle 'Y'
Hence Y = alpha + beta
d) The converse of (b). Split up angle ADE into two by drawing a line (make it parallel to only ONE line, either AB or EF) through D. Make it parallel to, for example, AB. Using alternate angles, then one of the angle in ADE will be equal to alpha. Hence, the other angle must be beta. But angle DEF = beta. Therefore EF is parallel to line through D (alternate angles equal) which means it's parallel to AB

Ah thanks, I thought of constructing a line to do this question but I assumed that I was supposed to work with what I was given.

 

[calamebe]

I have a different solution to everyone here, my answer: http://m.imgur.com/nXOg1g8

That's what I love about geometry, the variety of ways to solve 1 problem. Also sorry for bad handwriting.

 

[Arucerious]

So...new question

 

[calamebe]

I'm not too sure whether my answer is correct, also I'm not exactly sure what the question is asking for. I think that the angle the either the biggest it can be or the smallest it can be can keep getting infinitely closer to 0° or 180° (As if it is >180°, it will no longer be a convex polygon and if it equals 180°, then it will be a straight angle and therefore a triangle). So I wrote my answer as an inequality, though as i said I'm not entirely confident. Anyway here is my answer: m.imgur.com/VcBiHba