1. Section 7.5 Proving Triangle Proportions
Friday, October 20, 2017Friday, October 20, 2017
Warm Up 𝑫 𝑨 , 𝟐 (𝑨𝑩𝑪𝑫)
𝑫 (𝟎 , 𝟎) , 𝟐 (𝑨𝑩𝑪𝑫) A D C B

2. Corresponding s Postulate
Example 1.
Given: DE ∥ BC
Prove: 𝐴𝐷 𝐷𝐵 = 𝐴𝐸 𝐸𝐶
Statements
Reasons
1. DE ∥ BC
Given
2. m∠ADE = m∠ABC
Corresponding s Postulate
3. m∠AED = m∠ACB
Corresponding s Postulate
AA Similarity
4. ADE  ABC
5. 𝐴𝐷 𝐴𝐵 = 𝐴𝐸 𝐴𝐶
Corresponding side of similar triangles are proportional.
6. AD + DB = AB
Segment Addition Postulate

3. Segment Addition Postulate
Example 1
Given: DE ∥ BC
Prove: 𝐴𝐷 𝐷𝐵 = 𝐴𝐸 𝐸𝐶
Statements
Reasons
7. AE + EC = AC
Segment Addition Postulate
8. 𝐴𝐷 𝐴𝐷+𝐷𝐵 = 𝐴𝐸 𝐴𝐸+𝐸𝐶
Substitution (5, 6 and 7)
9. AD(AE + EC) = AE(AD+DB)
Cross Products
10. AD ∙ AE + AD ∙ EC = AE ∙ AD +AE ∙ DB
Distributive Property
11. AD ∙ AE - AD ∙ AE+ AD ∙ EC =
Subtraction Property
AE ∙ AD − AD ∙ AE +AE ∙ DB

4. 13. AD∙𝐸𝐶 DB∙𝐸𝐶 = AE∙𝐷𝐵 DB∙EC Division Property
Example 1
Given: DE ∥ BC
Prove: AD DB = AE EC
Statements
Reasons
12. 𝐴𝐷∙EC=AE∙DB
Simplify
13. AD∙𝐸𝐶 DB∙𝐸𝐶 = AE∙𝐷𝐵 DB∙EC
Division Property
14. AD DB = AE EC
Simplify

5. Triangle Proportionality
If 𝐷𝐸 ∥ 𝐵𝐶 , then 𝐴𝐷 𝐷𝐵 = 𝐴𝐸 𝐸𝐶

6. Example 2
Prove the length of 𝑆𝑇 .
Statements
Reasons
1. RSV  RTU
Given
2. RSV and RTU are corresponding angles
Definition of Corresponding Angles.
Converse of Corresponding Angles Theorem
3. 𝑆𝑉 ∥ 𝑇𝑈
4. RVS  RUT
Corresponding Angles Theorem
5. ΔRSV  ΔRTU
Angle Angle Similarity

7. Corresponding sides of similar triangles are proportional
Example 2
Prove the length of ST.
Statements
Reasons
6. 𝑅𝑆 𝑅𝑇 = 𝑆𝑉 𝑇𝑈
Corresponding sides of similar triangles are proportional
7. 𝑅𝑆 =10
Given
8. 𝑆𝑉 =8
Given
9. 𝑇𝑈 =12
Given
𝑅𝑇 = 8 12
Substitution (Steps 6, 7, 8, and 9)

8. Example 2 Prove the length of 𝑆𝑇 . 11. 8∙ 𝑅𝑇 =10∙12 Cross Multiply
Statements
Reasons
11. 8∙ 𝑅𝑇 =10∙12
Cross Multiply
12. 8∙ 𝑅𝑇 =120
Simplify
∙ 𝑅𝑇 8 =
Division Property
14. 𝑅𝑇 =15
Simplify
15. 𝑅𝑆 + 𝑆𝑇 = 𝑅𝑇
Segment Addition

9. Substitution (Steps 7 and 14)
Example 2
Prove the length of 𝑆𝑇 .
Statements
Reasons
𝑆𝑇 =15
Substitution (Steps 7 and 14)
−10 + 𝑆𝑇 =15 −10
Subtraction Property
18. 𝑆𝑇 =5
Simplify

10. Check for proportionality
Example 3
Prove ΔABW ∼ ΔPQW. A W B P Q 20 25 10 8
Statements
Reasons
1. 𝐴𝑊 =25
Given
2. 𝐵𝑊 =20
Given
3. 𝑄𝑊 =8
Given
4. 𝑃𝑊 =10
Given
5. 𝐵𝑊 𝑄𝑊 ≟ 𝐴𝑊 𝑃𝑊
Check for proportionality

11. Substitution (Steps 1, 2, 3, 4, & 5)
Example 3
Prove ΔABW ∿ ΔPQW. A W B P Q 20 25 10 8
Statements
Reasons ≟
Substitution (Steps 1, 2, 3, 4, & 5)
· 10 ≟ 25 · 8
Cross Multiply
= 200
Simplify
9. m∠AWB = m∠PWQ
Vertical Angles
10. ΔABW ∼ ΔPQW
Side Angle Side Similarity