7.4 Notes Parallel Lines and Proportional Parts

Learning Goals: I can use proportional parts within triangles and with parallel lines.

Proportional Parts Within Triangles

Example 1 Find SU.

Find BY.

Example 2

In ⊿𝐷𝐸𝐹, 𝐷𝐻 = 18, 𝐻𝐸 = 36, and 𝐷𝐺 =1

2𝐺𝐹. Determine whether 𝐺𝐻 ∥ 𝐹𝐸.

In ⊿𝑊𝑋𝑌, 𝑋𝑌 = 15, 𝑌𝑍 = 25, 𝑊𝐴 = 15, and 𝐴𝑍 = 32. Determine whether 𝑊𝑋 ∥ 𝐴𝑌.

Triangle Midsegment

Example 3 In the figure, DE and EF are midsegments of ΔABC. Find AB.

Example 4 In the figure, DE and DF are midsegments of ΔABC. Find BC.

Proportional Parts of Parallel Lines

Example 5

a.) In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.

b.) In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x.

Example 6 Find x and y. Find a and b.