You are Here: Home >< Maths

# Plane Euclidean Geometry Watch

1. I have been working through this book (Plane Euclidean Geometry) and am at around chapter four. However, I was very curious about the first exercise, which asks you to prove:
i) Every triangle is congruent to itself
ii) If triangle ABC is congruent to triangle A'B'C', then A'B'C' is congruent to ABC
iii) If ABC is is congruent to A'B'C', and A'B'C' is congruent to A''B''C'', then ABC is congruent to A''B''C''.

How do you prove these? Is it enough to say for i) AB=AB, AC=AC,
angle BAC=angle BAC, triangles are congruent by SAS, or am I missing something?

These results must be proved using only the following axioms
1) It is possible to draw exactly one line through any two points
2) All straight angles (180) are equal to each other
3) If a straight line cuts two straight lines m,n so that the interior angles on one side add up to less than one straight angle, the lines m,n meet on that side
4)If X,Y lie on the same segment with AX=AY, then X=Y
Also, if A,B lie on the same side of line PQ with angle BAX=angle BAY, then A,X,Y lie on one straight line
5) Two triangles ABC and A'B'C' are congruent if AB=A'B', AC=A'C' and angle BAC=angle B'A'C'

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 1, 2010
Today on TSR

### Oxford interview invitations

When can you expect yours?

### Official Cambridge interview invite list

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.