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2. 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°.

3. Corresponding sides and corresponding angles - Wikipedia

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

   The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established in that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle ∠C corresponds to (equals) angle ∠K, ∠D corresponds to ∠L, ∠A ...

4. AA postulate - Wikipedia

   en.wikipedia.org/wiki/AA_postulate

   In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180 ...

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. Triangle - Wikipedia

   en.wikipedia.org/wiki/Triangle

   All pairs of congruent triangles are also similar, but not all pairs of similar triangles are congruent. Given two congruent triangles, all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. This is a total of six equalities, but three are often sufficient to prove congruence ...

7. Transversal (geometry) - Wikipedia

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

   If the angles of one pair of corresponding angles are congruent, then the angles of each of the other pairs are also congruent. In the various images with parallel lines on this page, corresponding angle pairs are: α=α 1, β=β 1, γ=γ 1 and δ=δ 1.

8. 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

9. Euclidean geometry - Wikipedia

   en.wikipedia.org/wiki/Euclidean_geometry

   Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles unless the angle specified is a right angle. Triangles are congruent if they have all three sides equal (SSS), two sides and the angle between them equal (SAS), or two angles and a side equal (ASA) (Book I, propositions 4, 8, and 26).