Topic 7 Review: Similar Figures

Similar figures

Two figures are similar if there exists a sequence of similarity transformations that maps one figure onto another

Sequence of similarity transformations often include a dilation

Properties of similar figures

Same shape but possibly different sizes

-all corresponding lengths proportional

-all corresponding angles congruent

Scale factor

Ratio of proportionality

Symbol of similarity

~

TRIANGLE SIMILARITY POSTULATES

AA(angle-angle)

SAS(side-angle-side)

SSS(side-side-side)

Unlike congruency, what must be in the same ratio?

Pairs of corresponding sides

Perimeter, area, and volume in similar figures

Are related to the ratio of corresponding sides

Perimeter a/ perimeter b = scale factor

Area a/area b = (scale factor)²

Volume a/ volume b = (scale factor)³

SEGMENT PARALLEL TO A SIDE THEOREM

A segment // to a side of a triangle forms a triangle similar to the original triangle

If a segment intersects two sides of a triangle such that a triangle similar to the original is formed, the segment is parallel to the third size of the original

SIDE SPLITTER THEOREM

Segment parallel to a side in a triangle divides the two sides it intersects proportionally

CENTROID THEOREM

The centroid of a triangle divides each median in a 1:2 ration, with the longer segment having a vertex as one of its endpoints

MIDSEGMENT THEOREM

Segment joining the midpoints of the two sides of a triangle (a midsegment) is parallel to the opposite side, and its length is equal to ½ the length of the opposite side

ALTITUDE TO THE HYPOTENUSE OF A RIGHT TRIANGLE THEOREM

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to the original triangle

LEG 1 MEAN PROPORTIONAL THEOREM

Seg 1/ leg 1 = leg 1/ hyp

LEG 2 MEAN PROPORTIONAL THEOREM

Seg 2/ leg 2 = leg 2 / hyp

ALTITUDE MEAN PROPORTIONAL THEOREM

Seg 1 / alt. = alt. /seg 2