Question

Given: AABC with = CB

Prove: DE AC
7
What is the missing step in this proof?
OA. ZBAC ZACB
OB.
ZBDE ZDEB
ZADE ZDEC
OD. ZBAC BDE
OE. ZABC ZDBE
O C.

Answer 1

ACDE; ZABC ZDBE

Step-by-step explanation:

In the given problem, it's initially stated that ∠ABC is congruent to ∠CAB. From this information, using the corresponding angles postulate or the angle addition postulate, we can deduce that ∠ADE is congruent to ∠DEC. Additionally, given that AC is congruent to CB, it implies that AD is congruent to DC due to the Isosceles Triangle Theorem.

Therefore, by combining these angle and side relationships, triangles ADE and DEC are congruent by the Angle-Side-Angle (ASA) postulate, proving ACDE. Regarding the missing step, ZABC and ZDBE are corresponding angles in congruent triangles ADE and DEC, respectively. This correspondence of angles in congruent triangles ensures the equality of these angles, validating the statement ZABC ZDBE.

Starting from the information that ∠ABC is congruent to ∠CAB, it implies that the angles ∠ADE and ∠DEC are congruent. This deduction is due to the angles being corresponding in the congruent triangles ADE and DEC. Furthermore, the given information AC = CB leads to AD = DC by the Isosceles Triangle Theorem.

By proving that two angles and a side in one triangle are congruent to two angles and the corresponding side in another triangle, we establish the congruence of triangles ADE and DEC using the ASA postulate. Thus, the proof concludes with the establishment of ACDE. As for the missing step, ZABC and ZDBE correspond as angles in congruent triangles ADE and DEC, respectively, ensuring their equality, confirming the relationship ZABC ZDBE.

Answer 2

Answer: It seems that the missing step in this proof would be option "OB" ZBDE ZDEB ZADE ZDEC,

Step-by-step explanation:

It's showing that the angles are equal and the angles are congruent. The reason is that by definition, congruent angles have the same degree measure and by using the Angle-Angle Similarity Criterion we can prove that if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.

It is important to note that this statement can only be used when the two figures are similar and it is not sufficient for congruency. Therefore, a missing step in this proof would be to prove that the figures are similar before using the Angle-Angle Similarity Criterion.

The statement given is "AABC with = CB" and the conclusion is "DE AC." The question is asking for the missing step in the proof that shows how these two statements are related.