Postulates & Theorems - chapter 7

Question 1

ANGLE-ANGLE (AA) SIMILARITY POSTULATE: If 2 angles of one triangle are congruent to 2 angles of another triangle, then ….

Answer 1

the triangles are similar. (post. 7-3-1)

Question 2

SIDE-SIDE-SIDE (SSS) SIMILARITY THEOREM: If 3 sides of one triangle are proportional to 3 corresponding sides of another triangle, then ….

Answer 2

the triangles are similar. (theo. 7-3-2)

Question 3

SIDE-ANGLE-SIDE (SAS) SIMILARITY THEOREM: If 2 sides of one triangle are proportional to 2 sides of another triangle and their included angles are congruent, then ….

Answer 3

the triangles are similar. (theo. 7-3-3)

Question 4

TRIANGLE PROPORTIONALITY THEOREM: If a line parallel to a side of a triangle intersects the other 2 sides, then ….

Answer 4

it divides those sides proportionally. (theo. 7-4-1)

Question 5

CONVERSE OF THE TRIANGLE PROPORTIONALITY THEOREM: If a line divides 2 sides of a triangle proportionally, then ….

Answer 5

it is parallel to the third side. (theo. 7-4-2)

Question 6

TWO-TRANSVERSAL PROPORTIONALITY COROLLARY: If 3 or more parallel lines intersect two transversals, then ….

Answer 6

they divide those transversals proportionally. (theo. 7-4-3)

Question 7

TRIANGLE ANGLE BISECTOR THEOREM: An angle bisector of a triangle divides the opposite side into two segments whose lengths are ….

Answer 7

proportional to the lengths of the other 2 sides. (theo. 7-4-4)

Question 8

PROPORTIONAL PERIMETERS AND AREAS THEOREM: If the similarity ratio of 2 similar figures is a/b, then the ratio of their perimeters is …. (a), and the ratio of their areas is …. (b)

Answer 8

(a) a/b

(b) a^2/b^2