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Mikal is proving that AE ≅ CE . Triangles A B E and C D E are connected at point E. Angles A B E and E D C are right angles. The lengths of A C and D C are congruent. Which reason does the ♣ represent in Mikal’s proof? SAS SSS ASA AAS the
the picture cut off the final answer AAS

Mikal is proving that AE ≅ CE . Triangles A B E and C D E are connected at point E. Angles A B E and E D C are right angles. The lengths of A C and D C are cong class=

Answer :

Patterson16

Answer:

D) AAS

Step-by-step explanation:

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ΔABE and ΔCDE are right triangles that are formed by the segments [tex]\mathbf{\overline{AC}}[/tex]

and [tex]\mathbf{\overline{BD}}[/tex] and therefore, have an equal acute angle, making them similar.

Correct response:

The ♣ represents;

  • AAS

Details of the process used for finding the correct response

The statements in the two column proof are;

1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex]; Given

3. ∠ABE ≅ ∠CDE; All right angles are 90°, which makes them congruent.

5.  ∠AEB ≅ ∠CED; By vertical angles theorem

6. ΔABE ≅ ΔCDE; By Angle-Angle-Side, AAS, rule of congruency.

AAS rule of congruency states that two triangles are congruent if two

angles and the nonincluded or opposite sides of two triangles are equal,

then the two triangles are congruent.

∠ABE and ∠AEB and the non included side [tex]\overline{AB}[/tex]  in ΔABE are equal to the

angles ∠CDE and ∠CED and the included side [tex]\overline{CD}[/tex] in ΔCDE, therefore,

ΔABE is congruent to ΔCDE by AAS.

Learn more about congruency theorems here:

https://brainly.com/question/11356969

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