The following two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally:

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Martebi Martebi · Answer 1 · 2022-07-19T20:25:47+02:00

The missing statement are:

4. ∠B ≅ ∠B; Reflexive Property of Equality.

5. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate.

The missing statement are number 4 and 5.

If we say that 4. ∠B ≅ ∠B; Reflexive Property of Equality then:

∠B ≅ ∠B,

Note that there are two triangles, which are ΔABC and ΔDBE and we also have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B + ∠BCA = 180°

Hence, ∠BED = ∠BCA Substitution property of equality

That birth ΔABC ~ ΔDBE,which is Angle Angle Similarity Postulate

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