Sections 4.3 - 4.5
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Sections 4.3 - 4.5 Triangle Congruence
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Sections 4.3 - 4.5. Triangle Congruence. Example 1:. Assume that G is the midpoint of . Explain whether or not ∆FGJ and ∆HGJ are congruent. ∆FGJ ∆HGJ by SSS. On Your Own 1:. Decide whether or not the congruent statement is true. Explain your reasoning. a. b. by SSS. - PowerPoint PPT Presentation
Transcript of Sections 4.3 - 4.5
Sections 4.3 - 4.5
Triangle Congruence
Example 1:
Assume that G is the midpoint of . Explain whether or not ∆FGJ and ∆HGJ are congruent.
FH
∆FGJ ∆HGJ by SSS
On Your Own 1:
Decide whether or not the congruent statement is true. Explain your reasoning.
a. b.
by SSS Not by SSS
Example 2:
Use the diagram to name the included angle between the given pair of sides.
a. b.c.
H HIG HGI
On Your Own 2:
Use the diagram to name the included angle between the given pair of sides.
a. b.c.
GIJ HGI J
Leg:
Hypotenuse:
congruent
Longest side of a right triangle and opposite the right angle
2 shorter sides of a right triangle
Example 3a
Decide whether enough information is given to prove that the triangles are congruent by using SAS.
Example 3b
Decide whether enough information is given to prove that the triangles are congruent by using SAS.
Not enough info
Example 4:
Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem.
B) B and D are both right angles. C is the midpoint of .
A)
BD
On Your Own 4:
Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem.
c. d.
Example 5:
NO AAAYes AAS
Yes ASA
Identify congruent trianglesCan the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.
a. b. c.
On Your Own 5:
Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.
c. TSW WVT? d.
NO
Yes ASA
Combining All the Congruence Theorem Postulates
Are the 2 triangles congruent?
AAS congruence theorem
Nope, AAA does not insure that triangles congruent
ASA congruence theorem
Reflex
ive P
rope
rtyHL congruence theorem
e)
AAS congruence theorem
B
A C
D
E F
AAS congruence theoremf)
g)
No theorem to prove the 2 triangles congruent
h)Reflexive
Property
SSS congruence theorem
Ref
lexi
ve P
rope
rty
SAS congruence theoremi)
Decide whether enough information is given to prove that the triangles are
congruent (STATE THE CONGRUENCE
THEOREM!)
j. k.
SAS
SSS
Decide whether enough information is given to prove that the triangles are
congruent (STATE THE CONGRUENCE
THEOREM!)
l. m.
NO
NO
EXTRA PRACTICE
Explain how you can prove that the indicated triangles are congruent using the given postulate or theorem.
a.
b.
c.
Practice problems
State the third congruence that is needed to prove that ∆ DEF ∆ ABC, using the given postulate or theorem.
1.
2.
3.
E B
Tell whether you can use the given information to show that
∆ JKL ∆ RST.
4.
5.
6.
7.
NO
Yes AAS
Yes ASA
NO
