Question

two triangles are considered
if their corresponding
angles are equal and their corresponding sides are
proportional.
two triangles are
if all
corresponding sides and angles are equal.
the
theorem states that in
a right triangle, the square of the hypotenuse is equal to
the sum of the squares of the legs.
two triangles are considered similar if their
corresponding angles are
and their corresponding sides are proportional.
the criteria used to prove triangle similarity include
, sas, and sss.
two triangles are congruent if all corresponding sides
and
are equal.
the congruence postulates include sss, sas, asa, and
.
the pythagorean theorem states that in a right triangle,
the square of the
is equal
to the sum of the squares of the legs.
the triangle proportionality theorem states that a line
parallel to one side of a triangle divides the other two
sides
.
the converse of the triangle proportionality theorem
proves that two lines are
when the sides are divided proportionally.
the
postulate states that if
all three sides of two triangles are equal, the triangles
are congruent.

Explanation:

1. For the first blank, the definition of similar triangles is when corresponding angles are equal and sides are proportional.
2. Congruent triangles have all corresponding sides and angles equal.
3. The Pythagorean Theorem relates the sides of a right - triangle.
4. Similar triangles criteria include AA (Angle - Angle), SAS (Side - Angle - Side), and SSS (Side - Side - Side).
5. Congruent triangles have all corresponding sides and angles equal.
6. Congruence postulates include SSS, SAS, ASA (Angle - Side - Angle), and AAS (Angle - Angle - Side).
7. Pythagorean Theorem: square of the hypotenuse.
8. Triangle Proportionality Theorem: divides the other two sides proportionally.
9. Converse of Triangle Proportionality Theorem: lines are parallel.
10. SSS postulate for congruent triangles.

Answer:

1. similar
2. congruent
3. Pythagorean
4. equal
5. AA
6. angles
7. AAS
8. hypotenuse
9. proportionally
10. parallel
11. SSS