Geometry Chapter 6 6 5 USE PROPORTIONALITY THEOREMS
- Slides: 35
Geometry Chapter 6 6 -5: USE PROPORTIONALITY THEOREMS
Warm-Up Solve 1. ) for x. The polygons in each pair are similar. 2. )
Use Proportionality Theorems Objective: Students will be able to use proportions to find the missing side lengths and prove parallel lines in similar triangles. Agenda Triangle Proportionality Theorems for Parallel Lines Examples involving the Theorems
Triangle Proportionality Theorem 6. 4 – Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Example 1
Example 1
Example 2
Example 2
Triangle Proportionality Theorem 6. 5 – Converse of the Triangle Proportionality Theorem: If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Example 3
Example 3
Example 3
Example 4
Example 4
Example 4
Triangle Proportionality Theorem 6. 6: If three parallel lines intersect two transversals, then they divide the transversals proportionally
Example 5
Example 5
Example 5
Example 6 Find the value of x in the given diagram.
Example 6 Find the value of x in the given diagram.
Triangle Proportionality Theorem 6. 7: If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the side lengths of the other two sides.
Example 7
Example 7
Example 8 Find the value of x in the given diagram.
Example 8 Find the value of x in the given diagram.
Example 8 Find the value of x in the given diagram.
Final Practice Find the value of x in the diagram given.
Final Practice Find the value of x in the diagram given.
Final Practice
Final Practice
Final Practice Find the value of x in the given diagram.
Final Practice Find the value of x in the given diagram.
Final Practice Find the value of x in the given diagram.
Final Practice Find the value of x in the given diagram.