Geometry Postulates and Theorems
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SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of another triangle and the sides including these angles are in proportion,
then the triangles are similar.
SSS Similarity Theorem
If all corresponding sides of two triangles are in proportion
then the triangles are similar.
If a segment is parallel to one side of a triangle and intersects in the other two sides,
then it divides those sides proportionally.
If the midpoints of two sides of a triangle are joined by a segment,
then the segment is parallel to the third side of the triangle and its length is half the length of the third side of the triangle and its length is half the length of the third side of the triangle.
If two similar two-dimensional figures have corresponding lengths whose ratio is a : b,
then the ratio of all corresponding linear measures is a : b , the ratio of their perimeter is a : b, and the ratio of their areas is a2 : b2
If two similar three-dimensional figures have corresponding lengths whose ratio is a : b
then the ratio of all linear measures is a : b, the ratio of their surface areas (S.A.) is a a2 : b2, and the ratio of their volumes (V) is a3 : b3.