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Name the parts of their sides that DFG and EHG share. PowerPoint Presentation
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Name the parts of their sides that DFG and EHG share. - PowerPoint PPT Presentation


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Identify the overlapping triangles. . Parts of sides DG and EG are shared by DFG and EHG . . These parts are HG and FG , respectively. Using Corresponding Parts of Congruent Triangles. LESSON 4-7. Additional Examples.

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slide1

Identify the overlapping triangles.

Parts of sides DG and EG are shared by DFG and EHG.

These parts are HG and FG, respectively.

Using Corresponding Parts of Congruent Triangles

LESSON 4-7

Additional Examples

Name the parts of their sides that DFG and EHG share.

Quick Check

slide2

Label point M where ZX intersects WY, as shown in the diagram. ZWYX by CPCTC if ZWMYXM.

Look at MWX. MWMX by the Converse of the Isosceles Triangle Theorem.

Look again at ZWMand YXM.  ZMWYMX because vertical angles are congruent, MWMX, and by subtraction  ZWMYXM, soZWMYXM by ASA.

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YXW

Prove: ZWYX

You can prove these triangles congruent using ASA as follows:

Quick Check

slide3

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 XWYZ. Because XWZ and YZW are right angles,XWZ YZW. WZZW, by the Reflexive Property of Congruence.

Therefore, XWZYZW by SAS. WXZZYW by CPCTC, andXPWYPZ because vertical angles are congruent.

Therefore, XPWYPZ by AAS.

Using Corresponding Parts of Congruent Triangles

LESSON 4-7

Additional Examples

Write a paragraph proof.

Given: XWYZ, XWZ and YZW are right angles.

Prove: XPWYPZ

Quick Check

slide4

1. BCE DCA 1. Reflexive Property of Congruence

2. CACE, BADE 2. Given

7. CBCD 7. Definition of congruence

8. CBECDA 8. SAS

9. CBE CDA 9. CPCTC

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 CDA.

Plan: CBE CDA by CPCTC if CBECDA.

This congruence holds by SAS if CBCD.

Statements Reasons

Proof:

3. CA = CE, BA = DE 3. Congruent sides have equal measure.

4. CA – BA = CE – DE 4. Subtraction Property of Equality

5. CA – BA = CB, 5. Segment Addition PostulateCE – DE = CD

6. CB = CD 6. Substitution

Quick Check