3.5 overlapping triangles objective: after studying this lesson you will be able to use overlapping...
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3.5 Overlapping Triangles3.5 Overlapping Triangles
Objective: After studying this lesson you will be able to
use overlapping triangles in proofs.
Let’s look at this problem. At first we might try to prove . We could then say that angles D and C are congruent because of CPCTC
Given:
Prove:
DB AC
AD BC
CC
AA BB
DD
D C EE
ADE BCE
But there is not enough information.
We have to find two other angles to which D and C belong. Then we can prove the triangles congruent and their corresponding parts.
We can make overlapping triangles easier.
CC
AA BB
DDEE
We can color the two triangles we are going to use.
We can draw the triangles separately.
BBBBAA AA
DD CC
Given:
Prove: CE BDStatement Reason
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
EE
CC
DD
AA
BB
AC ABAE AD
Given:
Prove:
G is the midpoint of FH
Statement Reason
1.
2.
3.
4.
5.
6.
7.
8.
1.
2.
3.
4.
5.
6.
7.
8.
MM
JJHH
GG
FH MJFF
KK
GHJ KJH
K is the midpoint of MJGJ HK
Summary:Summary:
Don’t let overlapping Don’t let overlapping triangles confuse you. triangles confuse you. Name ways that you can Name ways that you can help to see where the help to see where the overlapping triangles are.overlapping triangles are.
Homework: worksheetHomework: worksheet