Download Angle Relationships for Parallel Lines Definition: a transversal is a

Geometric Properties Review
March 5, 2014
Angle Relationships for Parallel Lines
Definition: a transversal is a line that crosses two parallel lines.
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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.
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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.
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Property: the measures of alternate angles are
equal.
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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.
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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:
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2
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• 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.
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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:
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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.
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