Check for Understanding: Parallelograms and Proofs Name: -----------For #1-4, tell if the statement is Always, Sometimes, or Never true.

1. A square is a parallelogram. 3. A rhombus is a square. _

2. A trapezoid is a parallelogram. 4. A parallelogram is a rectangle. _

5. Is it a parallelogram? _ (Draw counterexample if possible) 6. Is it a parallelogram? _

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Use the phrases and theorems from the Word Bank tocomplete this two-column proof. j)dH

7. Given: GHIJ is a rhombus. ?Prove: L 1 ::::L3 J - I

Alternate Interior .6 Thm.GHIJ is a paraJlelogram.Trans. Prop. of ::::L2 == L3

Statements Reasons

1. GHIJ is a rhombus. 1. Given .2.8. 2. rhomb. - CJ

3. GRII JI 3. CJ - opp. sides II

4. L 1 = L2 4. b.

5. c. 5. rhomb. - each diag. bisects opp . .6

6.L1 = L3 6. d.

Prove: L.BCD =:: LABF ~----?D

8. Given: ABDF and FBCD are parallelograms.

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Statements Reasons

1. ABDF and FBCD are parallelograms. Given

2. LBCD =:: L.DFB

3. DF=::AB Opposite sides in a parallelogram are parallel.

4. LDFB =:: LABF

5. LBCD =:: LABF Transitive Property

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Independent Practice

Using Properties of Parallelograms in a ProofWrite a two-column proof.

-~1Theorem 6-2-2Given: ABCD is a parallelogram,Prove: LBAD = LDCB. LABC = LCDAProof:

Statements Reasons

1. ABCD is a parallelogram. 1.1 I- -- - 2.1 I2. AB :: CO, DA -- BC- - 3.1 I3. BD -- 80

4. l:::.BAD:: l:::.DCB 4.1 I5. LBAD:: LOCB 5.1 I- - 6.' I6. AC:: AC7. MBC ....l:::.COA 7·1 I

8. LABC:: LCDA 8.' I

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Sil Given: GH]lVand/KLAJ are-~

parallelograms. _G L

Prove: LG::: LLProof:

Statements Reasons1. I 1. Given2. I 2. 0 ~ opp. d ::3. I 3. Vert. Lt Thm.4. I 4. Trans. Prop. of :::::

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