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Mathematics, 18.11.2019 20:31 minaale

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in δabc shown below, segment de is parallel to segment ac:

triangles abc and dbe where de is parallel to ac

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:

statement reason
1. line segment de is parallel to line segment ac, 1. given
2. line segment ab is a transversal that intersects two parallel lines, 2. conclusion from statement 1.
3.
4. ∠b ≅ ∠b, 4. reflexive property of equality
5.
6. bd over ba equals be over bc, 6. converse of the side-side-side similarity theorem

which statement and reason accurately completes the proof?
3. ∠bde ≅ ∠bac; corresponding angles postulate
5. δbde ~ δbac; angle-angle (aa) similarity postulate

3. δbde ~ δbac; corresponding angles postulate
5. ∠bde ~ ∠bac; angle-angle (aa) similarity postulate

3. ∠bde ≅ ∠bac; congruent angles postulate
5. δbde ~ δbac; angle-angle (aa) similarity postulate

3. ∠bde ≅ ∠bac; congruent angles postulate
5. δbde ~ δbac; side-angle-side (sas) similarity postulate

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