Geometry (MEANING OF SIMILARITY - THEOREMS)

Why are all equilateral triangles similar?

ASA Similarity Postulate

THEOREM 5-3

If three sides of one triangle are proportional to three sides of another triangle, then the triangles are similar. (SSS for similar triangles)

THEOREM 5-2

If two sides of one triangle are proportional to two sides of another triangle and included angles are equal, then the triangles are similar. (SAS for similar triangles)

In a pair of similar polygons, corresponding angles are congruent.

always

Right isosceles triangles are similar.

always

Which of the triangle(s) shown is similar to triangle c? https://internationalvla.sooschools.com/media/g_geo_ccss_2016/5/groupi20.gif

e,f,b and h

ABC ~ ADE https://internationalvla.sooschools.com/media/g_geo_ccss_2016/5/groupi19.gif BC is parallel to DE. AB = x, AD = 5, AC = x+1 and AE = 7. The value of x is

2.5

ABC ~ ADE https://internationalvla.sooschools.com/media/g_geo_ccss_2016/5/groupi19.gif BC parallel to DE. BC = 6, DE = 9 Which of the following could be the lengths of AB and BD respectively?

4 and 2

Acute triangles are similar.

sometimes

Isosceles triangles are similar.

sometimes

Right triangles are similar.

sometimes

ABC ~ ADE https://internationalvla.sooschools.com/media/g_geo_ccss_2016/5/groupi19.gif AC = 4, AE = 7, AD = 10, what is the length of AB?

5 5/7

ABC ~ ADE https://internationalvla.sooschools.com/media/g_geo_ccss_2016/5/groupi19.gif If BC is parallel to DE, then all of the following are equivalent to each other except

AE/AC