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Provide the missing reasons with proof. Given: AB/DB = CB/EBProve: ∆ABC~∆DBE

Provide The Missing Reasons With Proof Given ABDB CBEBProve ABCDBE class=

Sagot :

Answer:

Statement 1. AB/DB = CB/EB

Reason 1: Given

Statement 2: ∠ABC = ∠BDE

Reason 2: Vertical angles

Statement 3: ∆ABC~∆DBE

Reason 3: SAS (side - angle - side)

Explanation:

It is given that AB/DB = CB/EB. So, we can say that the ratio of side AB to DB is equal to the ratio of side CB to EB. This made these sides similar.

Additionally, ∠ABC and ∠BDE are vertical angles because they are opposite angles formed when two lines intersect. Vertical angles have the same measure so, ∠ABC = ∠BDE.

Now, we can say that the triangles ABC and DBE are similar by SAS (Side-Angle-Side). Because two sides are similar and the angle between them is congruent.

Therefore, the answer is

Statement 1. AB/DB = CB/EB

Reason 1: Given

Statement 2: ∠ABC = ∠BDE

Reason 2: Vertical angles

Statement 3: ∆ABC~∆DBE

Reason 3: SAS (side - angle - side)

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