kkaasshh
contestada

Fill in the missing reason for the proof.
A) SSS Congruence Theorem
B) SSS Similarity Theorem
C) AA Similarity Postulate
D) SAS Congruence Postulate

Fill in the missing reason for the proof A SSS Congruence Theorem B SSS Similarity Theorem C AA Similarity Postulate D SAS Congruence Postulate class=

Respuesta :

Answer: C) AA Similarity Postulate



Step-by-step explanation: Given a triangle ACD.

BE || CD.

Also we are given Statement and reasons

<A = <A

<ACD ≅ <ABE

<ADC ≅ <AEB

We need to provide ΔABE similar to ΔACD.

From the given table of statement and reasons, we can see that three pairs of angles in triangles ΔABE and ΔACD are congruent.

Therefore, we can say that

ΔABE similar to ΔACD is similar by Angle Angle similarity postulate.

Therefore, correct option is C option.

C) AA Similarity Postulate



The [tex]\Delta ABE \sim \Delta ACD[/tex] by AA Similarity Postulate. Option (C) is correct.

Further Explanation:

The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.

There are many similarity rules and are as follows.

1. Angle Angle (AA)

2. Side Side Side (SSS)

3. Side Angle Side (SAS)

Given:

The options are as follows,

A) SSS Congruency Theorem

B) SSS Similarity Theorem

C) AA Similarity Theorem

D) SAS Congruence Postulate

Explanation:

The [tex]\overline {BE} \parallel \overline {CD}.[/tex]

In triangle ACD and triangle ABC.

1. [tex]\angle A \cong \angle A[/tex]

2. [tex]\angle ACD \cong \angle AEB[/tex]

3. [tex]\angle ADC = \angle AEB[/tex]

The [tex]\Delta ABE \sim \Delta ACD[/tex] by AA Similarity Postulate

Hence, [tex]\Delta ABE \sim \Delta ACD[/tex] by AA Similarity Postulate. Option (C) is correct.

Option (A) is not correct.

Option (B) is not correct.

Option (C) is correct.

Option (D) is not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangle

Keywords: congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, congruent triangle, similarity theorem, SSS congruency theorem, SSS similarity theorem, AA similarity postulate, SAS congruency postulate.

Otras preguntas