Sections 4.3 - 4.5
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Transcript of Sections 4.3 - 4.5
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Sections 4.3 - 4.5
Triangle Congruence
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Similar Triangles
We know from previous sections, that two triangles are similar if:
AA (2 sets of corresponding angles are congruent)
SAS (2 corresponding sides have the same scale factor and one set of angles between the 2 sides are congruent)
SSS (3 sets of corresponding sides are proportional)
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If 3 sides of one triangle are congruent to 3 sides of another, then the 2 triangles are congruent.
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SSS
If the corresponding sides of two triangles are proportional (all have the same scale factor), then the triangles are ___________.
If the corresponding sides of two triangles are congruent (S.F. = 1), then the triangles are ___________.
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a. b.
SSS:Decide whether or not the
congruent statement is true by SSS. Explain your reasoning.
6
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If 2 sides and the included angle of a triangle are congruent to the corresponding parts of another, then the triangles are congruent.
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SAS
If 2 sets of corresponding sides proportional (all have the same scale factor) and 1 set of corresponding angles are congruent, then the triangles are ___________.
If the corresponding sides of two triangles are congruent (S.F. = 1), then the triangles are ___________.
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SAS:Decide whether or not the congruent statement is true by SAS. Explain your reasoning.
c. d.
Yes No
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If 2 angles and the included side of a triangle are congruent to the corresponding parts of another, then the triangles are congruent.
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c. d. A
B
E
C
D
ASA: Decide whether or not the congruent statement is true by ASA. Explain your reasoning.
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If 2 angles and the non- included side of a triangle are congruent to the corresponding parts of another, then the triangles are congruent.
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AAS:
NOYes ASA
Decide whether or not the congruent statement is true by AAS. Explain your reasoning.
c. d.
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If the hypotenuse and a leg of a right triangle are congruent to the corresponding parts of another, then the triangles are congruent.
Leg:
Hypotenuse: Longest side of a right triangle and opposite the right angle
2 shorter sides of a right triangle
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B) B and D are both right angles. C is the midpoint of .
A)BD
HL:Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem.
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SSA / ASS
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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.
1. is TSW WVT? 2. 3.
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Warm Up:
Use the diagram to name the included angle between the given pair of sides.
a. b. c.H HIG HGI
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On Your Own 2:
Use the diagram to name the included angle between the given pair of sides.
a. b. c.GIJ HGI J
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EXTRA PRACTICE
Explain how you can prove that the indicated triangles are congruent using the given postulate or theorem.a.
b.
c.
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Practice problemsState the third congruence that is needed to prove that ∆ DEF ∆ ABC, using the given postulate or theorem.
1.
2.
3.
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Tell whether you can use the given information to show that
∆ JKL ∆ RST.
4.5.6.7.
NO
Yes AAS
Yes ASA
NO