Question

Given: ΔABC with
Prove:




Statement Reason
1. given
2. Addition Property of Equality
3. using common denominators
4. AB = AD + DB
CB = CE + EB segment addition
5. Substitution Property of Equality
6. ∠ABC ≅ ∠DBE Reflexive Property of Congruence
7. ΔABC ~ ΔDBE SAS similarity criterion
8. Corresponding angles of similar triangles are congruent.
9. If the corresponding angles formed by two lines cut by a transversal are congruent, then the lines are parallel.


What is the missing step in this proof?
A.
∠BAC ≅ ∠ACB
B.
∠BDE ≅ ∠DEB
C.
∠ADE ≅ ∠DEC
D.
∠BAC ≅ ∠BDE
E.
∠ABC ≅ DBE

Answer 1

Given :- ΔABC with AD/DB = CE/EB

To Prove :- DE || AC .

Solution :-

Step 1) :-

→ AD/DB = CE/EB (given)

Step 2) :-

→ AD/DB + 1 = CE/EB + 1 (Addition Property of Equality)

Step 3) :-

→ (AD + DB)/DB = (CE + EB)/EB (using common denominators)

Step 4) :-

→ AB = AD + DB

→ CB = CE + EB (segment addition)

Step 5) :-

→ AB/DB = CB/EB (Substitution Property of Equality) { putting step 4 in step 3 .}

Step 6) :-

→ ∠ABC ≅ DBE (common angle.)

Step 7) :-

→ ΔABC ~ ΔDBE (SAS similarity criterion) { corresponding sides are in same ratio and angle between them is equal. }

Step 8) :-

→ ∠BAC ≅ ∠BDE (Corresponding angles of similar triangles are congruent.)

Step 9) :-

→ DE || AC (If the corresponding angles formed by two lines cut by a transversal are congruent, then the lines are parallel.)

therefore we can conclude that, Option (E) ∠ABC ≅ DBE is the missing step in this proof .

Learn more :-

in triangle ABC seg DE parallel side BC. If 2 area of triangle ADE = area of quadrilateral DBCE find AB : AD show that B...

https://brainly.in/question/15942930

2) In ∆ABC seg MN || side AC, seg MN divides ∆ABC into two parts of equal area. Determine the value of AM / AB

https://brainly.in/question/37634605

Answer 2

Answer:segment addition

5.

Substitution Property of Equality

6. ∠ABC ≅ ∠DBE Reflexive Property of Congruence

7.

SAS criterion for similarity

Step-by-step explanation: