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Geometric Properties Review March 5, 2014 Angle Relationships for Parallel Lines Definition: a transversal is a line that crosses two parallel lines. 2 3 4 1 2 3 1 In the diagram at left, the angles labelled with the same number are called corresponding angles, because they occupy the same positions relative to the points of intersection between the transversal and the parallel lines. > > 4 Property: the measures of corresponding angles are equal. In the next diagram, the angles labelled with the same number are called alternate angles, because they are on opposite sides of the transversal. 1 2 Property: the measures of alternate angles are equal. > 2 1 On each side of the transversal, the angles labelled 1 and 2 are called co-interior angles, because they are between the parallel lines and are on the same side of the transversal. > Property: co-interior angles are supplementary (i.e., they add up to 180°). Similar and Congruent Triangles Definition: two figures are similar if they have the same shape. In similar polygons, each interior angle in one is equal to the corresponding angle in the other, and the length of each side of one is the same multiple of the length of the corresponding side of the other. The constant multiple is called the scale factor. Conditions for similar triangles: two triangles are similar if any of the following is true: 1 2 3 1 2 MPM2D 3 • SSS – all three pairs of corresponding sides are proportional (i.e., related by the same scale factor) • SAS – two pairs of corresponding sides are proportional, and the contained angles (the angles between these sides in each triangle) are equal • AA – two of the angles of one triangle are equal to two angles of the other. Page 1 of 2 Geometric Properties Review March 5, 2014 Definition: two figures are congruent if they have the same shape and size. In congruent polygons, corresponding interior angles are equal, and corresponding sides are equal. Conditions for congruent triangles: two triangles are congruent if any of the following is true: • • • SSS – all three pairs of corresponding sides are equal SAS – two pairs of corresponding sides are equal, and the contained angles (the angles between these sides in each triangle) are equal ASA – two of the angles of one triangle are equal to two angles of the other, and the sides between the two angles in each triangle are equal. MPM2D Page 2 of 2