Geometry 7 4 Parallel Lines and Proportional Parts
![Geometry 7. 4 Parallel Lines and Proportional Parts • Triangle Proportionality Theorem (Theorem 7. Geometry 7. 4 Parallel Lines and Proportional Parts • Triangle Proportionality Theorem (Theorem 7.](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-1.jpg)
![Example • In the figure, AE || BD. Find the value of x. x+5 Example • In the figure, AE || BD. Find the value of x. x+5](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-2.jpg)
![Theorem 7. 5 • If a line intersects two sides of a triangle and Theorem 7. 5 • If a line intersects two sides of a triangle and](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-3.jpg)
![Example • Determine whether DE || BC. • Yes because 6/3 = 8/4 A Example • Determine whether DE || BC. • Yes because 6/3 = 8/4 A](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-4.jpg)
![Theorem 7. 6: Triangle Midsegment Theorem • Midsegment: Midsegment A segment with endpoints that Theorem 7. 6: Triangle Midsegment Theorem • Midsegment: Midsegment A segment with endpoints that](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-5.jpg)
![Example • Refer to the figure and Example #3 on page 407 • The Example • Refer to the figure and Example #3 on page 407 • The](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-6.jpg)
![Corollary 7. 1 • If 3 or more || lines intersect 2 transversals, then Corollary 7. 1 • If 3 or more || lines intersect 2 transversals, then](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-7.jpg)
![Example • In the figure, a || b || c. Find the value of Example • In the figure, a || b || c. Find the value of](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-8.jpg)
![Corollary 7. 2 • If 3 or more || lines cut off segments on Corollary 7. 2 • If 3 or more || lines cut off segments on](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-9.jpg)
![Homework #48 • p. 411 13 -18, 21 -29 odd, 32 -38 even, 54 Homework #48 • p. 411 13 -18, 21 -29 odd, 32 -38 even, 54](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-10.jpg)
- Slides: 10
![Geometry 7 4 Parallel Lines and Proportional Parts Triangle Proportionality Theorem Theorem 7 Geometry 7. 4 Parallel Lines and Proportional Parts • Triangle Proportionality Theorem (Theorem 7.](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-1.jpg)
Geometry 7. 4 Parallel Lines and Proportional Parts • Triangle Proportionality Theorem (Theorem 7. 4) • If a line is || to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths. C B A D E
![Example In the figure AE BD Find the value of x x5 Example • In the figure, AE || BD. Find the value of x. x+5](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-2.jpg)
Example • In the figure, AE || BD. Find the value of x. x+5 C x B 6 A D 8 E
![Theorem 7 5 If a line intersects two sides of a triangle and Theorem 7. 5 • If a line intersects two sides of a triangle and](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-3.jpg)
Theorem 7. 5 • If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is || to the third side. C then BD || AE A B D E
![Example Determine whether DE BC Yes because 63 84 A Example • Determine whether DE || BC. • Yes because 6/3 = 8/4 A](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-4.jpg)
Example • Determine whether DE || BC. • Yes because 6/3 = 8/4 A 6 8 D 3 B E 4 C
![Theorem 7 6 Triangle Midsegment Theorem Midsegment Midsegment A segment with endpoints that Theorem 7. 6: Triangle Midsegment Theorem • Midsegment: Midsegment A segment with endpoints that](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-5.jpg)
Theorem 7. 6: Triangle Midsegment Theorem • Midsegment: Midsegment A segment with endpoints that are midpoints of two sides of the triangle. • A midsegment of a triangle is || to one side of the triangle and its length is one-half the length of the third side. A D B E C
![Example Refer to the figure and Example 3 on page 407 The Example • Refer to the figure and Example #3 on page 407 • The](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-6.jpg)
Example • Refer to the figure and Example #3 on page 407 • The example uses the midpoint formula, the slope formula and the distance formula to verify coordinates of midpoint, parallelism, and lengths of segments.
![Corollary 7 1 If 3 or more lines intersect 2 transversals then Corollary 7. 1 • If 3 or more || lines intersect 2 transversals, then](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-7.jpg)
Corollary 7. 1 • If 3 or more || lines intersect 2 transversals, then they cut off the transversals proportionally. X A B C D E F
![Example In the figure a b c Find the value of Example • In the figure, a || b || c. Find the value of](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-8.jpg)
Example • In the figure, a || b || c. Find the value of x. • 20 15 9 12 x a b c
![Corollary 7 2 If 3 or more lines cut off segments on Corollary 7. 2 • If 3 or more || lines cut off segments on](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-9.jpg)
Corollary 7. 2 • If 3 or more || lines cut off segments on one transversal, then they cut off segments on every transversal.
![Homework 48 p 411 13 18 21 29 odd 32 38 even 54 Homework #48 • p. 411 13 -18, 21 -29 odd, 32 -38 even, 54](https://slidetodoc.com/presentation_image_h/97b30902310fd148d80e857d9826b275/image-10.jpg)
Homework #48 • p. 411 13 -18, 21 -29 odd, 32 -38 even, 54 -55
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