objectives: 1) to use the side-splitter theorem 2) to use the triangle- angle bisector theorem 8-5...

OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

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OBJECTIVES:1) TO USE THE SIDE-SPLITTER THEOREM

2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM

8-5 Proportions in TrianglesM11.C.1

Side-Splitter Theorem 8-4If a line is parallel to one side of a triangle

and intersects the other two sides, then it divides those sides proportionally.

Page 3: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

ExampleUse the side-splitter theorem to solve for x.

Page 4: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

Example

Find y.

Page 5: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

CorollaryIf three parallel lines intersect two

transversals, then the segments intercepted on the transversals are proportional.

Page 6: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

Example: Use Corollary The segments joining the sides of trapezoid

RSTU are parallel to its bases. Find x and y

Page 7: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

ExampleSolve for x and y.

Page 8: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

Triangle-Angle-Bisector TheoremIf a ray bisects an angle of a triangle, then it

divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Page 9: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

Example: Use the triangle-angle bisector

Use the triangle-angle bisectortheorem to find x.

Page 10: OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

Example

Use the triangle-angle-bisector theorem to find y.

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