Lesson 5: 7-5: Parallel Lines and Proportional Parts

1. How can you use proportionality to solve problems?
2. Are the lengths of two parallel segments that have their endpoints on two other parallel lines proportional?
3. Are the lengths of two parallel segments that have their endpoints on two intersecting lines proportional?
4. What is a midsegment of a triangle?

Midsegment of a Triangle

G.SRT.4
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G.CO.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)

If a line is parallel 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. A midsegment is a segment with endpoints that are the midpoints of two sides of the triangle. The midsegment is parallel to one side of the triangle.

Photographers have many techniques at their disposal that can be used to add interest to a photograph. One such technique is the use of a vanishing point perspective, in which an image with parallel lines, such as train tracks, is photographed so that the lines appear to converge at a point on the horizon.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections by creating their own pictures with vanishing points (p. 537, Example 4).

Unit 7 Assessment

Mastery Based Assessment

Textbook in class

Access online textbook and resources through class link.