SIMILARITY: A REVIEW A REVIEW Moody Mathematics. Midsegment: a segment that joins the midpoints of 2 sides of a triangle? Moody Mathematics.

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Presentation transcript:

SIMILARITY: A REVIEW A REVIEW Moody Mathematics

Midsegment: a segment that joins the midpoints of 2 sides of a triangle? Moody Mathematics

A Midsegment is parallel to one side of the triangle and half of its length. Moody Mathematics

x 16 Find x, the length of the midsegment X = 8 Moody Mathematics

8 midsegments x y 7 20 Find x, y, z z Moody Mathematics

8 midsegments x y 7 20 x=8, y=10, z=14 x=8, y=10, z=14 z Moody Mathematics

Property of Proportions #1 Moody Mathematics

Property of Proportions #2 Moody Mathematics

Property of Proportions #3 Moody Mathematics

Property of Proportions #4 Moody Mathematics

Property of Proportions #5 Moody Mathematics

PRACTICE:

Definition: Polygons are similar if: 1. Corresponding Angles are congruent 2. Corresponding sides are in proportion Moody Mathematics

x 12 y w Find w, x, y, z in these similar trapezoids z Moody Mathematics

x 12 y w z Moody Mathematics

x 12 y w W=60 o z X=9.375 Y=9.6 Z=120 o Moody Mathematics

Similar Triangles Moody Mathematics

AA Postulate: If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 2 triangles are similar. Moody Mathematics

SSS~ Postulate: If all 3 sides of two triangles are in proportion, then the triangles are similar. Moody Mathematics

SAS~ Postulate: If 2 sides of two triangles are in proportion and their included angles are congruent, the triangles are similar. Moody Mathematics

PRACTICE:

Similar? Yes by SAS~ Yes by SAS~ Moody Mathematics

Similar? Yes by SSS~ Moody Mathematics

Similar? Yes by AA Moody Mathematics

62 o 48 o 50 o Similar? No! Corresponding angles are not congruent. No! Corresponding angles are not congruent. 68 o 70 o Moody Mathematics

8 4 7 x Find x Moody Mathematics

4 6 9 Find x x Moody Mathematics