Download What are the 4 ways to prove triangles congruent?

4.2-4.3 Proofs: Proving Triangles Congruent
Principles of Geometry
Objective: To prove triangles congruent
What are the 4 ways to prove triangles congruent?
1.
3.
2.
4.
What are the 2 ways that don’t give you enough information?
1.
2.
Review: Can you prove the following s congruent?
Mark the triangles appropriately. If yes, give reason and write a congruence
statement. If no, write “Not Possible.”
∆𝐶𝐴𝑇 ≅ _______________ by ___________
Tips:
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First, mark the picture and determine why the triangles are congruent.
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Then be sure to mention each marked item (congruent sides or congruent angles) in your proof.
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Look for the basics: Vertical Angles OR Shared Side
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Look for more complicated information in GIVEN: Parallel Lines, Angle Bisector, Segment Bisector,
Midpoint, Perpendicular Lines, Perpendicular Bisector, Right Angles, Median, Altitude, etc.
1)
Given:
Prove:
1.
̅̅̅̅̅ bisects XAY
𝑨𝑴
X  Y
 AMX   AMY
Statement
Reason
̅̅̅̅̅ bisects XAY
𝑨𝑴
X  Y
1. Given
2.
2.
3.
3.
4.
4.
2) Given:
̅̅̅̅
P is the midpoint of 𝑨𝑩
AB
 APX   BPY
Prove:
1.
Statement
Reason
P is the midpoint of
̅̅̅̅
𝑨𝑩
AB
1.
2.
2.
3.
3.
4.
4.
3)
Given:
Prove:
̅̅̅̅ ∥ ̅̅̅̅
𝑨𝑩
𝑪𝑫
BD
 ABC   CDA
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.