Question

Compete the following proof by filling in the blanks)

Statements Reasons

In ∆ ADF and ∆ BCE

1. ∠ADF=_________ corresponding angles

2. ∠AFD= ∠BEC ________________________

3. AD=______ opposite sides of a parallelograms

4. ∆ ADF ≅ ∆BCE __________________________

5. ar (∆ADF) = ar (∆BCE) congruent figures have equal area

6.But ar (□ ABCD) = ar (∆ ADF) + ar (□ABCF)

7.ar (□ ABCD)=_________________+ ar (□ ABCF)

8. ar (□ ABCD) =​

Answer 1

1. ∠ADF= <BCE corresponding angles

2. ∠AFD= ∠BEC corresponding angles

3. AD=BC opposite sides of a parallelograms

4. ∆ ADF ≅ ∆BCE AAA

5. ar (∆ADF) = ar (∆BCE) congruent figures have equal area

6.But ar (□ ABCD) = ar (∆ ADF) + ar (□ABCF)

7.ar (□ ABCD)=ar (∆ ADF)+ ar (□ ABCF)

8. ar (□ ABCD) =​ar (□ ABCF)