Download 4 - Garnet Valley School District

Geometry A Unit 4 Day 5 Notes
Using Congruent Triangles
I. Although "CPCTC" makes it sound complicated, the idea is a reasonable next step
after proving triangles congruent.
A. "Real World" example of CPCTC.
A person (AB) wearing a hat stands perfectly straight at the edge of a river and looks
down so that the point where the end of his cap is visible meets the other edge of the river
B
(point C).
D
C
A
Then, remaining perfectly straight, they turn and locate a point behind them at which
the end of their cap meets the ground. (point D). The person thinks that if they can run
and jump from D to , that they would be able to run and jump across the river. Do you
think they are right?
1. Before we answer, we should consider the triangles in the picture above and decide if
they are congruent.
2. If we can use other parts to say they are congruent triangles, then we can say
AD = DC since they are matching parts and "Corresponding Parts of Congruent
Triangles are Congruent.
B
Proof:
12
Given:  1 =  2, AB  CD
Prove: AC = AD
1. _____________________ 1. ______________________
2. _____________________ 2. ______________________
3. _____________________ 3.  lines form 4  90  's
4. _____________________ 4. Reflexive
5. ABC  ABD
5. ______________________
6. _____________________ 6. ______________________
C
D
A
II. CPCTC and what it says about isosceles triangles.
A. Base Angles Theorem
In an isosceles triangle, the angles opposite the congruent sides (THE BASE
ANGLES) are congruent.
B. Converse of the Base Angles Theorem
In a triangle, if two angles are congruent, then the sides across from those angles
are congruent.
Ex: Find the missing angle or side, or solve for the variable.
3
1)
2)
36o
27o
4
2
1
 1 = __________  2 = ___________
5
3)
 3 = ____________  4 = __________
4)
9y
3zo
11y
20x – 20
o
13x + 8
36o
o
5y + 30
x = ____________  5 = _____________
y = __________ z = __________
III. Equal sides means equal angles as it applies to equilateral triangles.
A. We have already done this problem before…
Find the measure of each angle.
1
 1 = _______
 2 = _______
2
3
 3 = _______
B. But we now know that angles across from equal sides are equal. So…
Find the measure of each angle.
4
 4 = _______
 5 = _______
 6 = _______
6
5
C. We can now apply this in more complicated drawings.
Find the measure of each angle.
B
1.
2.
7
A
1
2
 1 = ______
3
4
 2 = _______
C
 5 = ________
 3 = _______  4 = _______
 6 = _______
 ABC = __________
 7 = ________
Skills Practice
HW: p. 232 #8-10, 14, 15, 17, 18 (see help for #’s 14, 15, 17, 18 online)
p. 239 #11-16; p. 242 #42, 43, 54, 55
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5