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Question
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Complete the proof.
Given: AB · BE = CB · BD
Prove: ΔABC ~ ΔDBE
Two triangles A B C and D B E are formed by intersecting segments. Segment A E intersects Segment C D at point B. A segment connects points A and C. Another segment connects points D and E.
Statements Reasons
1 AB dot BE = CB dot BD 1 given
2 CB/BE = AB/BD 2. Property of ?
3 angle ABC ~= angle DBE 3 ?
4 triangle ABC ~ angle DBE 4 ?
Statements Reasons
1. AB · BE = CB · BD 1. Given
2. AB/BD = CB/BE 2. Property of Proportions (cross-multiplying)
3. ∠ABC ≅ ∠DBE 3. Corresponding angles for parallel lines AB and DE
4. ΔABC ~ ΔDBE 4. Angle-Angle Similarity Postulate (AA similarity)