Download 4-7 Using Corresponding Parts of Congruent Triangles

Using Corresponding Parts of Congruent Triangles
LESSON 4-7
Additional Examples
Name the parts of their sides that
DFG and
EHG share.
Identify the overlapping triangles.
Parts of sides DG and EG are shared by
DFG and
EHG.
These parts are HG and FG, respectively.
Quick Check
HELP
GEOMETRY
Using Corresponding Parts of Congruent Triangles
LESSON 4-7
Additional Examples
Write a Plan for Proof that does not use overlapping triangles.
Given: ZXW YWX, ZWX
Prove: ZW YX
YXW
Label point M where ZX intersects WY, as shown in the
diagram. ZW YX by CPCTC if ZWM
YXM.
You can prove these triangles congruent using ASA as follows:
Look at MWX. MW
Theorem.
MX by the Converse of the Isosceles Triangle
Look again at ZWM and YXM.  ZMW YMX because vertical
angles are congruent, MW MX, and by subtraction  ZWM YXM, so
ZWM
YXM by ASA.
Quick Check
HELP
GEOMETRY
Using Corresponding Parts of Congruent Triangles
LESSON 4-7
Additional Examples
Write a paragraph proof.
Given: XW YZ, XWZ and YZW are right angles.
Prove: XPW
YPZ
Plan: XPW
YPZ by AAS if WXZ ZYW. These
angles are congruent by CPCTC if XWZ
YZW.
These triangles are congruent by SAS.
Proof: You are given XW YZ. Because XWZ and YZW are right angles,
XWZ YZW. WZ ZW, by the Reflexive Property of Congruence.
Therefore, XWZ
YZW by SAS. WXZ ZYW by CPCTC, and
XPW YPZ because vertical angles are congruent.
Therefore,
XPW
YPZ by AAS.
Quick Check
HELP
GEOMETRY
Using Corresponding Parts of Congruent Triangles
LESSON 4-7
Additional Examples
Given: CA CE, BA DE
Write a two-column proof to show that CBE
Proof: Statements
Plan: CBE CDA by CPCTC if CBE
This congruence holds by SAS if CB CD.
Reasons
1. BCE DCA
2. CA CE, BA DE
3. CA = CE, BA = DE
4. CA – BA = CE – DE
5. CA – BA = CB,
CE – DE = CD
6. CB = CD
7. CB CD
8. CBE
CDA
9. CBE CDA
HELP
CDA.
CDA.
1. Reflexive Property of Congruence
2. Given
3. Congruent sides have equal measure.
4. Subtraction Property of Equality
5. Segment Addition Postulate
6. Substitution
7. Definition of congruence
8. SAS
9. CPCTC
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GEOMETRY