Geometry: A/S/N
Sometimes
The bisector of an angle of a triangle divides it into two similar triangles.
Never
The diagonals of a trapezoid bisect each other.
Always
Two isosceles right triangles are similar
Always
Two isosceles triangles are similar if a base angle of one is congruent to a base angle of another
Sometimes
Two isosceles triangles are similar if an angle of one is congruent to an angle of the other.
Always
Two isosceles triangles are similar if the vertex of one is congruent to the vertex angle of another.
Always
Two regular pentagons are similar.
Never
An equilateral triangle is similar to a scalene triangle.
Always
If a triangle is equilateral, then its equiangular.
sometimes
Rhombuses are similar
Always
If 2 similar convex polygons have sides with lengths in the ratio 1:1, they are congruent.
Always
If 2 triangles are similar, their corresponding alititudes have the same ratios as their perimeters.
Sometimes
If TRIANGLE ABC ~ TRIANGLE DEF and TRIANGLE DEF ~ TRIANGLE SOT, then AC=ST
Always
If a line is one of the trisectors of one side of a triangle and is parallel to a second side, then it is one of the trisects of the 3rd side
Never
If the ratio of the measures of a pair of corresponding sides of two similar polygons is 3:4, then the ratio of the perimeters is 5:6.
Always
If two angles are supplementary and congruent, they are right angles.
Sometimes
If two sides of one triangle are proportional to two sides of a second triangle, then the triangles are similar.
Always
In two triangles, if all 3 pairs of corresponding angles are proportional, then the triangles are similar.
Sometimes
If a quadrilateral is equilateral then its equiangular.
Always
Two right triangles are similar if the legs of one are proportional to the legs of another.
