Common Core: High School - Geometry › Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures
Consider the parallelogram below. From what you know about parallelograms and our theorems for congruence in triangles, prove that triangles and
are congruent.
Consider the two triangles below (ABE and CBE). Given that sides and
are equal and
bisects
, prove triangles ABE and CBD are congruent.
and
are equal and
bisects
, prove triangles ABE and CBD are congruent.
Choose the answer that describes similar triangles
Consider the group of line segments below. is parallel to
. What is the relationship between triangles
and
?
and
are parallel. Are triangles
and triangle
are similar? If so, solve for
.
Choose the answer that describes a congruent triangle
True or False: When considering right triangles, if two right triangles have a congruent hypotenuse and a congruent leg then these triangles are congruent.
True or False: The triangles below are similar, NOT congruent.
Triangle is similar to triangle
. Solve for
and
.
True or False: Triangles that have all three corresponding sides equal in length can still have differing corresponding angles, therefore triangles with all three corresponding sides equal in length are not guaranteed to be either similar or congruent.