Question

Given: ad ― ⁢ | | ⁢ bc ― prove: d ⁢ c = 6 units a diagram shows a parallelogram abcd. a diagonal ac is drawn. the length of ab is 6 units. statements reasons ad ― ⁢ | | ⁢ bc ― given ∠ dac ≅ ∠ bca alternate interior angles theorem ac ― ≅ ac ― reflexive property of congruence ∠ dca ≅ ∠ bac alternate interior angles theorem ? ? dc ― ≅ ba ― cpctc d ⁢ c = b ⁢ a definition of congruent sides d ⁢ c = 6 units substitution property of equality which step is missing?

a. △ dac ≅ △ bca by sas
b. △ dac ≅ △ bca by asa
c. △ dca ≅ △ bca by sas
d. △ dca ≅ △ bca by

Answer 1

To prove that dc = 6 units, we can use the fact that ad || bc and the corresponding angles are congruent. Using the corresponding angles theorem, we can conclude that ∆dac ≅ ∆bca. Therefore, the corresponding sides are congruent, giving us dc ≅ ba. Since we know that ba = 6 units, we can substitute this value to find dc = 6 units.

Step-by-step explanation:

To prove that dc = 6 units, we can use the fact that ad || bc and the corresponding angles are congruent. This means that we have two sets of alternate interior angles that are congruent: ∠dac ≅ ∠bca and ∠dca ≅ ∠bac.

Using the corresponding angles theorem, we can conclude that ∆dac ≅ ∆bca. Therefore, the corresponding sides are congruent, giving us dc ≅ ba. Since we know that ba = 6 units, we can substitute this value to find dc = 6 units.