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2. Corresponding sides and corresponding angles - Wikipedia

   en.wikipedia.org/wiki/Corresponding_sides_and...

   The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.

3. Congruence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Congruence_(geometry)

   AAS (angle-angle-side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180°.

4. Triangle - Wikipedia

   en.wikipedia.org/wiki/Triangle

   The included angle for any two sides of a polygon is the internal angle between those two sides.) If and only if three pairs of corresponding sides of two triangles are all in the same proportion, then the triangles are similar. [b] Two triangles that are congruent have exactly the same size and shape. All pairs of congruent triangles are also ...

5. Similarity (geometry) - Wikipedia

   en.wikipedia.org/wiki/Similarity_(geometry)

   If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1. However, some school ...

6. Hinge theorem - Wikipedia

   en.wikipedia.org/wiki/Hinge_theorem

   In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. [1]

7. Midpoint theorem (triangle) - Wikipedia

   en.wikipedia.org/wiki/Midpoint_theorem_(triangle)

   Hence by Side angle side. Therefore, the corresponding sides and angles of congruent triangles are equal = = = Transversal AC intersects the lines AB and CD and alternate angles ∠MAN and ∠DCN are equal. Therefore