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What is the missing statement in the proof? Scroll down to see the entire proof.


a ∠BDC≅∠ADB


b ∠BCA≅∠DCB


c ∠BAC≅∠BAD


d ∠DBC≅∠BAC

Done
Given: ΔABC with m∠ABC = 90° (view diagram)

Prove: AB2 + BC2 = AC2

Statement

Reason

1. Draw BD¯¯¯¯¯⊥AC¯¯¯¯¯ (view diagram).

construction

2. ∠ABC≅∠BDC

Angles with the same measure are congruent.

3.

Reflexive Property of Congruence

4. ΔABC~ΔBDC

AA criterion for similarity

5. BCDC=ACBC

Corresponding sides of similar triangles are proportional.

6. BC2 = AC × DC

cross multiplication

7. ∠ABC≅∠ADB

Angles with the same measure are congruent.

8. ∠BAC≅∠DAB

Reflexive Property of Congruence

9. ΔABC~ΔADB

AA criterion for similarity

What is the missing statement in the proof Scroll down to see the entire proof a BDCADB b BCADCB c BACBAD d DBCBAC Done Given ΔABC with mABC 90 view diagram Pro class=

Respuesta :

Answer: C. [tex]\angle BCA\cong \angle DCB[/tex] is the missing statement.

Explanation: Given: ΔABC with m∠ABC = 90° (view diagram)

Prove: [tex]AB^2 + BC^2 = AC^2[/tex]

Proof:  1. Draw [tex]BD\perp AC[/tex] (construction)

 2. [tex]\angle ABC\cong\angle BDC[/tex]  (Angles with the same measure are congruent.)

3. [tex]\angle BCA\cong \angle DCB[/tex] (Reflexive Property of Congruence)

4. [tex]\triangle ABC\sim \triangle BDC[/tex]  (AA criterion for similarity)

5. BC:DC=AC:BC  (Corresponding sides of similar triangles are proportional.)

 6.[tex]BC^2= AC\times DC[/tex]  (cross multiplication)----------(1)

7. [tex]\angle ABC\cong \angle ADB[/tex] (Angles with the same measure are congruent)

8. [tex]\angle BAC\cong \angle DAB[/tex] (Reflexive Property of Congruence)

9. [tex]\triangle ABC\sim \triangle ADB[/tex]  (AA criterion for similarity)

10.  AB:AD=AC:AB⇒[tex]AB^2=AC.AD[/tex] --------------(2)

equation (1) + equation (2) ⇒[tex]AB^2+BC^2= AC(DC+AD)[/tex]⇒[tex]AB^2+BC^2= AC^2[/tex]

The missing statement in the proof specified is given by: Option B: ∠BCA≅∠DCB

What is reflexive property of congruence?

The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.

For this case, the third step has bottom line: "Reflexive Property of Congruence"

And the fourth step then concludes that ΔABC~ΔBDC by AA criterion for similarity

Since in the second step, it was proven that ∠ABC≅∠BDC

So, in third step, we need to show another angle pair of ΔABC and ΔBDC being congruent so that fourth step applies angle-angle similarity, which needs to angles of two considered triangles to be congruent.
In triangles ΔABC and ΔBDC, the common angle is internal angle C.

Thus, by reflexive property, it is congruent to itself.

From triangle ABC, we get the notation for internal angle C as: [tex]\angle ACB \: or \: \angle BCA[/tex] (both will work)

From triangle BDC, we get the notation for internal angle C as:

[tex]\angle DCB \: or \: \angle BCD[/tex](both will work).

They are congruent. The second option is considering the angle C, thus:

∠BCA≅∠DCB (second option) is the missing statement.

Learn more about reflexive property of congruency here:

https://brainly.com/question/862440

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