Advanced Geometry
Learning Target 4.1: Congruence and Transformations
Two plane figures are ____________ if and only if one can be obtained from the other by rigid transformations.
What does this mean?
Example 1: Determining If Figures are Congruent
Use the definition of congruence above to determine whether the two figures are congruent. Justify.
a)
b)
Example 2: Finding a Sequence of Rigid Motions
For each pair of congruent triangles, find a sequence of rigid motions that maps one figure onto the other.
a)
b)
How could tracing paper help you determine if two triangles are congruent?
Practice:
1. Use the definition of congruence in terms of rigid motions to determine whether the two figures are
congruent and explain your answer.
a)
b)
c)
2. For each pair of congruent figures, find a sequence of rigid motions that maps one figure onto the other.
Describe the transformations you use.
a)
b)
c)
Notation:
When two triangles are congruent it is written as
. What 6 things does this tell us?
Corresponding Parts of Congruent Triangles are Congruent Theorem (CPCTC)
If two triangles are _____________, then corresponding __________ are congruent and corresponding
__________ are congruent.
Or conversely…
If all ________________ parts of two triangles are congruent, then the triangles are _______________.
Example 3: Using CPCTC
a) Given
, complete the following statements.
b)
. Find AB and
.
c)
d) Determine whether the given triangles are congruent. Explain.
. Find DF and
.
Practice:
3. Determine whether the given triangles are congruent. Explain your reasoning.
a)
b)
4. Find the value of the variable that results in congruent triangles.
a)
b)
5. Determine whether
based on the given information.
6. The figure shows a portion of the truss of a bridge.
a) Is it possible to determine
? Justify.
b) A student claims that B is the midpoint of
. Do you agree? Explain.
.