Download Triangle Congruence Proofs 1

Triangle Congruence Proofs 1
Objectives:
G.CO.8: Explain how the criteria for triangle congruence (ASA,SAS, SSS, and AAS) follow
from the definition of congruence in terms of rigid motions.
G.CO.7: Use the definition of congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
G.SRT.5: Use congruence and similarity criteria for triangles to solve problems and
prove relationships in geometric figures.
For the Board: You will be able to prove two triangles congruent using SSS, SAS, ASA, or AAS.
Bell Work:
1. Name the angle formed by AB and AC.
2. Name three sides of ΔABC.
3. ΔQRS  ΔLMN. Name all pairs of congruent corresponding sides.
Anticipatory Set:
Triangles can be shown to be congruent with less than the requirements of the definition.
Instead of having all 3 angles and all 3 sides of one triangle congruent to the corresponding 3 angles and 3
sides of another triangle, only certain combinations of 3 sides and/or angles are necessary.
What are the possible combinations of sides (S) and angles (A) which need to be investigated?
SSS, SAS, SSA, ASA, AAS, AAA
Complete the Constructing Congruent Triangles handout.
Instruction:
Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides
of a second triangle, then the two triangles are congruent.
Given: AB  XY, BC  YZ, AC  XZ
Conclusion: ΔABC  ΔXYZ
Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of a second
triangle, then the two triangles are congruent.
Given: AB  XY, <B  <Y, BC  YZ
Conclusion: ΔABC  ΔXYZ
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A
B
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Y
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Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are
congruent to two angles and the included side of a
second triangle, then the two triangles are congruent.
Given: <A  <X, AB  XY, <B  <Y
Conclusion: ΔABC  ΔXYZ
Angle-Angle-Side (AAS) Congruence Theorem
If two angles and the non-included side of one triangle
are congruent to two angles and the corresponding
non-included side of another triangle, then the two
triangles are congruent.
Given: <A  <X, <B  <Y, BC  YZ
Conclusion: ΔABC  ΔXYZ
Complete Handout 1 problems 1 – 8.
Reflexive Property of Congruence
For any real number a, a = a.
Segment Version
For any segment AB, AB  AB
Angle Version
For any <A, <A  <A.
Vertical Angle Theorem
If two angles are vertical angles, then they are congruent.
Complete Handout 1 problems 9 – 18.
Assessment:
Collect and grade Handout 1
Independent Practice:
Complete Handout 1
X
A
B
A
B
Y
C
Z
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Y
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Z