Using Corresponding Parts of Congruent Triangles

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Using Corresponding Parts of Congruent Triangles
GEOMETRY LESSON 4-7
Overlapping triangles share part or all of one or
more sides.
Some triangle relationships are difficult to see
because the triangles overlap. Overlapping
triangles may have a common side or angle. You
can simplify your work with overlapping triangles
by separating and redrawing the triangles.
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Using Corresponding Parts of Congruent Triangles
GEOMETRY LESSON 4-7
Identifying Common Parts
Name the parts of their sides that ?DFG and ?EHG
share.
Quick Check
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Using Corresponding Parts of Congruent Triangles
GEOMETRY LESSON 4-7
Planning a Proof
Write a Plan for Proof that does not use
overlapping triangles.
Given ?ZXW ? ?YWX, ?ZWX ? ?YXW Prove ZW ? YX
You can prove these triangles congruent using ASA
as follows
Quick Check
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Using Corresponding Parts of Congruent Triangles
GEOMETRY LESSON 4-7
Using Two Pairs of Triangles
Write a paragraph proof.
Given XW YZ, ?XWZ and ?YZW are right
angles. Prove XPW YPZ
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Using Corresponding Parts of Congruent Triangles
GEOMETRY LESSON 4-7
Separating Overlapping Triangles
Given CA CE, BA DE Write a two-column
proof to show that ?CBE ?CDA.
Plan ?CBE ?CDA by CPCTC if CBE CDA.
This congruence holds by SAS if CB CD.
Statements Reasons
Proof
3. CA BA CE DE 3. Subtraction Property of
Equality
4. CA BA CB, 4. Segment Addition Postulate
CE DE CD
5. CB CD 5. Substitution
Quick Check
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Using Corresponding Parts of Congruent Triangles
GEOMETRY LESSON 4-7
1. Identify any common sides and angles in
AXY and BYX. For Exercises 2 and 3, name a
pair of congruent overlapping triangles. State
the theorem or postulate that proves them
congruent. 2. 3. 4. Plan a
proof. Given AC BD, AD BC Prove XD
XC
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