Question

lesson 8.9
complete the two - column proof. use words and symbols from the box. each word and each symbol is used once.
parallelgram, congruent, de = bf, 1/2(bf)(cd), given, area △cdb
you are given: parallelogram abcd
prove: area △abd = area △cdb
statements

1. parallelogram abcd
2. ab || cd

3.

1. ab ≅ cd
2. ab = cd
3. 1/2(de)(ab)=1/2(de)(cd)
4. 1/2(de)(ab)=
5. area △abd=

reasons
1.

1. definition of a parallelogram
2. the distance between two parallel lines is always equal.
3. property of a parallelogram
4. definition of line segments
5. multiplication property
6. substitution
7. area formula of a triangle

Explanation:

Step1: State the given

Given

Step2: Identify height equality

$DE = BF$

Step3: Define congruence for equality

congruent

Step4: Substitute CD for AB

$\frac{1}{2}(DE)(CD)$

Step5: Apply triangle - area formula

area $\triangle CDB$

Answer:

1. Given
2. Definition of a parallelogram
3. $DE = BF$
4. Property of a parallelogram
5. Definition of congruent line - segments
6. Multiplication Property
7. $\frac{1}{2}(DE)(CD)$
8. area $\triangle CDB$