# Thread: [SOLVED] Congruency of lines?

1. ## [SOLVED] Congruency of lines?

Hi, i;m really stuck on my maths homework.
It's about congruency and stuff, but this is about proving that lines are the same?
Anyhoo, here's the question:

In the diagram, DX = XC, DV = ZC,and the lines AB and DC are parallel. Prove That:
a) AX = BX
b) AC = BD
c) triangles DBZ and CAV are congruent

my roughly drawn diagram to this question is here:
http://i825.photobucket.com/albums/z...ers3/maths.jpg

If you need help reading the diagram just ask me what the matter is.

Thankyou sooo much!!

2. From the given we see that $\Delta DXC$ is isosceles, so $m\left( {\angle XDC} \right) = m\left( {\angle XCD} \right)$.
By the use of alternate interiors angles we get $m\left( {\angle CDB} \right) = m\left( {\angle DBA} \right)\;\& \,m\left( {\angle DCA} \right) = m\left( {\angle CAB} \right)$
From that we see that $\Delta AXB$ is isosceles.

Surely you can finish it from all the above.

3. many thanks,

could you help with this one aswell

PQRS is a square and equilateral triangles PQA and RQB are drawn witgh A inside and B outside the square.

By considering triangles PQR and AQB, prove that AB is equal to PR.

Thankyouu

4. Originally Posted by doopers3
could you help with this one aswell
PQRS is a square and equilateral triangles PQA and RQB are drawn witgh A inside and B outside the square.
By considering triangles PQR and AQB, prove that AB is equal to PR.
If this is a new question, then by forum rules you must start a new thread.