( Picture for clearer question) Craig wants to prove that if quadrilateral ABCDhave diagonals that bisect each other, then it is a parallelogram. ABCDE Craig says: "I can prove that line AB// CD by establishing the congruence of a single pair of triangles." Which pair of triangles is Craig referring to, and which criterion should he use for establishing congruence?

ABCtriangle, A, B, C and \triangle CDA△CDAtriangle, C, D, A by angle-side-angle

B
\triangle ABC△ABCtriangle, A, B, C and \triangle CDA△CDAtriangle, C, D, A by side-angle-side

C
\triangle ABE△ABEtriangle, A, B, E and \triangle CDE△CDEtriangle, C, D, E by angle-side-angle

D
\triangle ABE△ABEtriangle, A, B, E and \triangle CDE△CDEtriangle, C, D, E by side-angle-side

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Answer :

OEERIVONAGO OEERIVONAGO · Answer 1

The segments [tex]\mathbf{\overline{AB}}[/tex] and [tex]\mathbf{\overline{CD}}[/tex] if the alternate interior angles formed by the

lines and the common transversal [tex]\overline{AC}[/tex] are equal.

Correct response:

The pair of triangles that being congruent can be used to prove that [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] are found as follows;

Statement [tex]{}[/tex] Reason

1. [tex]\overline{AE}[/tex] = [tex]\overline{EC}[/tex] [tex]{}[/tex] 1. Given

[tex]\overline{BE}[/tex] = [tex]\overline{DE}[/tex] [tex]{}[/tex]

2. ∠AEB ≅ ∠CED [tex]{}[/tex] 2. Vertical angles theorem

3. ΔABE ≅ ΔCDE [tex]{}[/tex] 3. SAS Side-Angle-Side rule of congruency

4. ∠BAE ≅ ∠DCE [tex]{}[/tex] 4. CPCTC

5. ∠BAE and ∠DCE are alternate interior ∠s 5. Definition

6. [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] [tex]{}[/tex] 6. Converse of alternate interior angles theorem

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

Therefore, the pair of triangles Craig is referring to and the criterion are;

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