Download Section 4.6 Corresponding Parts of Congruent

Section 4.6 Notes: Corresponding Part of Congruent Triangles (CPCTC) Notes
Goals of the lesson:
•
•
Identify related triangles and prove them congruent.
Show that pairs of angles or pairs of sides are congruent in congruent triangles.
Big idea of this lesson: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Homework: Review pg. 232-233 and Complete pg. 233-235 #2-6, 9, 10, 14, 15, 18, 23 plus complete #4 in
the notesWarm Up:
1.
We know that some congruence shortcuts work and others don’t. Circle the ones that work and put
at X through the ones that do not work.
2. Given the triangle at the right. Find the equation of the median to തതതത
‫ ܥܤ‬.
A
6
A : (2, 6)
4
2
B: (–6, 1)
B
5
5
2
4
C: (3, –5)
C
6
What is CPCTC?
Example 1: Given ∆‫ܦܧܨ∆ ≅ ܥܤܣ‬, find x and y and all the angles in both triangles. Justify your initial
equations.
B
D
(5y)°
E
(y2-50)°
A
30°
(x2+ x)°
F
C
തതതത ≅ ‫ܥܤ‬
തതതത ? Use a deductive argument to explain why they
Example 2: Given the following figure below. Is ‫ܦܣ‬
must be congruent.
Example 3: Mark the figure with the given information. Answer the question about segment or angle
congruence. If your answer is yes, write a paragraph proof explaining why. Remember to use your
reasoning strategies, especially apply previous conjectures and add an auxiliary line. If there is not enough
information to prove congruence, write “cannot be determined,” otherwise state which congruence short cut
you used.
Example 4: Mark the figure with the given information. Answer the question about segment or angle
congruence. If your answer is yes, write a paragraph proof explaining why. Remember to use your
reasoning strategies, especially apply previous conjectures and add an auxiliary line. If there is not enough
information to prove congruence, write “cannot be determined,” otherwise state which congruence short cut
you used.
Try on your own:
For Exercises 1-2, mark the figure with the given information. To demonstrate whether the segments or the
angles indicate are congruent, determine that two triangles are congruent. Then state which conjecture
proves them congruent.
1.
2.
3.
4.
Given ∆‫ܥܤܦ∆ ≅ ܧܤܣ‬, find all possible values for x. Justify your initial equation.
A
C
20°
B
(x2-x)°
35°
E
D