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Proving a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
Warm – Up
SWBAT: Prove a Quadrilateral is a Parallelogram
quad has 2 sets of opp. sides ||
quad has 2 sets of opp. sides
quad has one pair of opposite sides and ||
quad has 2 sets of opp. angles
quad has diags. bisecting each other
quad has 2 sets of cons. ∡s supplementary
6.
(by definition)
SWBAT: Prove a Quadrilateral is a Parallelogram Determining if a quadrilateral is a parallelogram
Analyzing a Diagram
a.
b.
SWBAT: Prove a Quadrilateral is a Parallelogram Determining if a quadrilateral is a parallelogram
Analyzing a Diagram
c.
d.
SWBAT: Prove a Quadrilateral is a Parallelogram Determining if a quadrilateral is a parallelogram
Analyzing a Diagram
e.
SWBAT: Prove a Quadrilateral is a Parallelogram
No; opp sides not Yes; opp sides ll Yes; a pair of opp sides and ll
Yes; diags bisect each other
No! Yes; a pair of opp sides and ll
Yes; opp sides Yes; opp s
SWBAT: Prove a Quadrilateral is a Parallelogram
Yes; opp sides ll
No
No
Yes; opp sides
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
Statements Reasons
1. 𝑫𝑬 ⊥ 𝑨𝑪 ; 𝑩𝑭 ⊥ 𝑨𝑪 1. Given
2. ∡𝑩𝑭𝑪 𝒂𝒏𝒅 ∡𝑫𝑬𝑨 𝒂𝒓𝒆 𝒓𝒕 ∡𝒔 2. ⊥ → 𝒓𝒕 ∡𝒔
3. 𝑨𝑬 𝑪𝑭, 𝑫𝑬 𝑩𝑭 3. Given
4. ∆ADE ∆BFC 4. SAS (3, 2, 3)
5. 𝑨𝑫 𝑪𝑩, ∡𝑫𝑨𝑬 ∡𝑩𝑪𝑭 5. CPCTC
6. 𝑨𝑫 ∥ 𝑪𝑩 6. Alt int ∡ s → ||
7. 1 pair of opp sides both
and || → (5, 6)
7. ABCD is a
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
Statements Reasons
1. 𝑩𝑫 bisects 𝑨𝑪 𝒂𝒕 𝑬, ∡𝑫𝑨𝑬 ∡𝑩𝑪𝑭 1. Given
2. 𝑬 𝒊𝒔 𝒕𝒉𝒆 𝒎𝒊𝒅𝒑𝒐𝒊𝒏𝒕 𝒐𝒇 𝑨𝑪 2. Seg bisector → midpoint
3. 𝑨𝑬 𝑪𝑬 3. midpoint → 2 ≅ 𝑠𝑒𝑔𝑠
4. ∡𝑫𝑬𝑨 ∡𝑩𝑬𝑪 4. Vertical s
5. ∆ADE ∆CBE 4. ASA (1, 3, 4)
6. 𝑫𝑬 𝑩𝑬 6. CPCTC
7. ABCD is a 7. diags. Bisect. each other → (3, 6)
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Write a Proof Involving Parallelograms
1. ACDF is a 1. Given
2. Def of a 2. FD CA, AF DC
3. FD CA, AF DC 3.
4. A D 4. 5. AFB ECD 5. Given 6. ∆AFB ∆DCE 6. ASA (4, 3, 5)
7. AB DE 7. CPCTC
8. FE CB 8. Subtraction Post (3, 7)
9. 9. FBCE is a
(8, 2)
OR
SWBAT: Write a Proof Involving Parallelograms
1. ACDF is a 1. Given
2. FD CA, AF DC 2.
3. A D 3.
4. AFB ECD 4. Given
5. ∆AFB ∆DCE 5. ASA (4, 3, 5)
6. AB DE , 𝐹𝐵 ≅ 𝐶𝐸 6. CPCTC
7. FE CB 7. Subtraction Post (2, 6)
8. 8. FBCE is a
(6, 7)
6 ways to prove that a quadrilateral
is a parallelogram.
SWBAT: Prove a Quadrilateral is a Parallelogram
6 ways to prove that a quadrilateral
is a parallelogram.
SWBAT: Prove a Quadrilateral is a Parallelogram
