Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Alva wants to prove that opposite sides in a parallelogram are congruent. A A B B C C D D E E Alva says: "I can prove this by establishing the congruence of a single pair of triangles." Which pair of triangles is Alva referring to, and which criterion should she use for establishing congruence? Choose 1 answer: Choose 1 answer: (Choice A) A △ A B C △ABCtriangle, A, B, C and △ C D A △CDAtriangle, C, D, A by angle-side-angle (Choice B) B △ A B C △ABCtriangle, A, B, C and △ C D A △CDAtriangle, C, D, A by side-angle-side (Choice C) C △ A B E △ABEtriangle, A, B, E and △ C D E △CDEtriangle, C, D, E by angle-side-angle (Choice D) D △ A B E △ABEtriangle, A, B, E and △ C D E △CDEtriangle, C, D, E by side-angle-side

Sagot :

The opposite sides of the parallelogram are congruent given that the

opposite triangles formed by the diagonals are congruent.

Response:

  • (Choice C) ΔABE and ΔCDE by angle-side-angle postulate.

How to prove that opposite sides of a parallelogram are congruent?

The vertices of the parallelogram in the question is; ABCD

The point of intersection of the diagonals AC and BD is the point E

By proving that ΔABE ≅ ΔCDE, we have;

∠BEA ≅ ∠CED by vertical angles theorem

∠EAB ≅ ∠ECD by alternate angles theorem

The diagonals of a parallelogram bisect each other, therefore;

[tex]\overline{AE}[/tex] =  [tex]\mathbf{\overline{EC}}[/tex]  

Therefore;

ΔABE ≅ ΔCDE by angle-side-angle, ASA, congruency rule;

Which gives;

[tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex] by CPCTC

The correct choice is therefore;

  • (Choice C) ΔABE and ΔCDE by angle-side-angle postulate

Learn more about the rules of congruency here:

https://brainly.com/question/12039641

https://brainly.com/question/17158967

View image oeerivona
copperdog1011

Answer:

ABC and triangle CDA by angle-side-angle

Step-by-step explanation:

got it right on khan I would have taken a screen shot but i accidentally went ahead before i could

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.