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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

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