8.6 proportion and similar triangles. theorem triangle proportionality theorem if a line is parallel...

8.6 Proportion and Similar Triangles

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8.6 Proportion and Similar Triangles

Theorem

Triangle Proportionality Theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the two sides proportionally.

Converse of the Triangle Proportionally Theorem

If a line divides two sides of a triangle proportionally, then the line is parallel to the remaining side.

BCDEEC

AD//

Theorem

If three parallel lines are intersected by two lines, then the lines are divided proportionally.

Theorem

If a ray bisects one angle of a triangle, then it divides the sides proportional with the sides they are touching.

Solve for x

Page 7: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Solve for x

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Page 8: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Show that DE // BC

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Page 9: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Show that DE // BC

975.9

2426

BCDEEC

AD//

Page 10: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Solve for x

Page 11: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Solve for x

948

Page 12: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Solve for x

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Page 13: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Solve for x

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Page 14: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Homework

Page 502 – 503

# 11 - 28

Page 15: 8.6 Proportion and Similar Triangles. Theorem Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other

Homework

Page 503 – 505

# 29 – 31,

34 – 37, 39,

41 – 50

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