Similar Triangles Flashcards
Define proportion.
An equation that states that two ratios are equal.
State the SAS SIMILARITY THEOREM.
If one angle of one triangle is congruent to on angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
Define polygon.
A closed plane figure with three or more sides.
How can you tell if two polygons are similar?
If:
1) corresponding angles are congruent
2) corresponding sides are in proportion.
State the relationship of the ratios of similar polygons.
scale factor: a/b
ratio of their perimeters: a/b
Ratio of areas: a squared times b squared
State the theorem about a ray bisecting an angle.
If a ray bisects and angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
State the PERIMETERS OF SIMILAR POLYGONS THEOREM.
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths (scale factor).
Define ratio.
A comparison of two numbers. Written as a/b or a:b
State the SSS SIMILARITY THEOREM.
If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
State the theorem about three parallel lines.
If three parallel lines intersect two transversals, then they divide the transversals proportionally.
Define center of dilation.
The fixed point in which a figure is enlarged or reduced with respect.
Scale factor hint
K= image over pre-image
State the AA SIMILARITY POSTULATE.
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
What is the scale factor for:
a) a reduction
b) an enlargement
A) 01
State the TRIANGLE PROPORTIONALITY THEOREM.
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
