# Questions tagged [congruences-geometry]

For questions about congruent geometric figures, e.g., determining whether one figure is congruent to another.

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### Divide in two congruence piece [closed]

Divide the shape in two congruence piece (cut it into two identical shape). I saw this problem in a geometry book and spend about 4 hours on it but I couldn't find a solution, so any advise would be ...
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### congruence of two triangles

if two corresponding sides of two triangles are equal and their medians drawn on the third sides are also equal, prove two triangles are congruent. I tried to solve it by extending the median by its ...
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### Find length of chord between two tangents and distance of chord from origin

I am trying to solve 2 questions Is there a way to find an equation for the length of a chord between two tangents in terms of the radius and distance of that chord to the external point? Is there a ...
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### Proving the ASA, SAS congruence of triangles in absolute geometry.

I am asked to prove the SAS (side-angle-side) and ASA(angle-side-angle) congruence of triangles in absolute geometry ( the geometry based in the axiom system of Euclides with the parallel postulate ...
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### If two of these segments have lengths 8 and 6, what are all possible lengths of the third segment?

Please help me for this question, I can't fully understand the problem and not sure where and how to start. In a plane, two congruent squares share a common vertex but have no other points in common ...
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### How to prove the similarity of two rectangles?

The task is this: On the ABCD rectangles AB,BC,CD,DA sides we took up P,Q,R,S points, so PR and QS are perpendicular to each other. Let's prove that the middle points of SP,PQ,QR,RS segments form a ...
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### Congruence of triangles: SSA criteria

It is well known that this criteria does not work in general. I am trying to answer to the following question if two triangles have two sides and the angle NOT between them equal, they are either ...
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### Can a L-shaped figure be divided into 5 congruent shapes?

Given a square, remove one quarter of it. Can the resulting L-shaped figure be divided into 5 congruent shapes? If not, how can we prove that fact? I tried using circles, triangles and smaller ...