The (Ultimate) Geometry Review Sheet Page 9
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TOPIC:
CONSTRUCTIONS
PRACTICE
1.
Copying segments
2.
Copying angles
3.
Bisecting angles
4.
Bisecting segments
5. Constructing perpendicular segments given a point on the line
6. Constructing perpendicular segments given a point not on the line
(For these two, try looking
here.)
7.
Copying triangles
8. Constructing altitudes of a triangle
9.
Constructing parallel lines through a point
10.
Dividing a segment into n congruent parts
SIMILAR TRIANGLES/POLYGONS
In a proportion, the product of the means is equal to the product of the extremes.
In a proportion, the means may be interchanged.
In a proportion, the extremes may be interchanged.
AA Postulate - When 2 angles of one triangle are congruent to 2 corresponding angles of the
other triangle, the two triangles must be similar
SSS Similarity Theorem - If the corresponding sides of two triangles are in proportion, then
the triangles must be similar.
SAS Similarity Theorem - In two triangles, if two pairs of corresponding sides are in
proportion, and their included angles are congruent, then the triangles are similar.
If two polygons are similar, then the ratio of the perimeters is the same as the ratio of similitude
(scale factor).
If two polygons are similar, then the ratio of the areas is the square of the ratio of similitude
(scale factor).
Triangle Proportionality Theorem - If a line parallel to one side of a triangle intersects the
other two sides, then it divides those sides proportionally.
If three or more parallel lines cut off congruent segments on one transversal, then they cut off
congruent segments on every transversal.
If three or more parallel lines intersect two transversals, then they cut off the transversals
proportionally.
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