SideSplitter Theorem in triangle Wikispaces（令人捧腹的笑话在三角形Wikispaces定理）.pdfVIP

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SideSplitter Theorem in triangle Wikispaces（令人捧腹的笑话在三角形Wikispaces定理）.pdf

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SideSplitter Theorem in triangle Wikispaces（令人捧腹的笑话在三角形Wikispaces定理）

Class Note Unit: 6.3 Proportional in triangles/parallel lines Choose an item. Name:___________________________________ Period:__________ Date:__________________ Proportional relationship in triangle and parallel lines The Side-Splitter Theorem states the proportional relationship in a triangle in which a line is parallel to one side while intersecting the other two sides. Side-Splitter Theorem in triangle: In ∆ABC, GH AB and GH intersects BC and A C . The segments of BC and A C are proportional: A G BH GC HC Side-Splitter Theorem in parallel lines: The Side-Splitter Theorem extends the proportion to three parallel lines intercepted by two transversals. If AB CD and EF , you can find x using the proportion: 2 3 7 x 2x = 21 Cross Products Property x = 10.5 Solve for x. Triangle-Angle-Bisector Theorem When a ray bisects the angle of a triangle, it divides the opposite side into two segments that are proportional to the other two sides of the triangle. In ∆DEF, EG bisects E. The lengths of DG and DF are proportional to DG GF their adjacent sides DF and EF : . DE EF To find the value of x, use the proportion 3 x . 6 8 6x = 24 Use the diagram on right to complete the proportion Prepared by Kin Chan - MHS Page 1 of 2 Use the figure at the right to complete each proportion. Algebra Solve for x. 1. 2. 3. Algebra Solve for x. 4. 5. 6. 7. 8. 9. 10. In ∆ABC, AB = 6, BC = 8, and AC = 9. a) The bisector of A meets BC at po