TODAY IN GEOMETRY…

Learning Target: 6.6 You will calculate missing sides of triangles using proportionality with parallel lines

Independent Practice

CH.6 TEST – WEDNESDAY/THURSDAY!

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.

Given that:Then:

𝑄

𝑆

𝑅𝑇

𝑈 𝑅𝑇𝑇𝑄

𝑅𝑈𝑈𝑆

EXAMPLE: In the diagram, , what is length

9

𝑅

4

6𝑆

𝑇

𝑈𝑄

Write a proportion using Triangle Proportionality Theorem

Substitute known values

Cross Multiply

PRACTICE: Find length

2015

12𝑍𝑌

𝑈 𝑊

Write a proportion using Triangle Proportionality Theorem

Substitute known values

Cross Multiply

𝑋

CONVERSE OF THE TRIANGLE PROPORTIONALITY THEOREM: If a line divides two sides of a triangle proportionally, then it is parallel to the third side. Given that:

Then:𝑄

𝑆

𝑅𝑇

𝑈

EXAMPLE: Determine whether .

10𝑅

28

20𝑆

𝑇

𝑈𝑄

Write a proportion using Triangle Proportionality Theorem

Substitute known values

Cross Multiply

16

PRACTICE: Determine whether

13.5 22.5

12𝑍

𝑌

𝑈 𝑊

Write a proportion using Triangle Proportionality Theorem

Substitute known values

Cross Multiply

𝑋

20

EXAMPLE: Find length

4 18

𝑍

𝑈

Write a proportion using Triangle Proportionality Theorem

Substitute known values

Cross Multiply

𝑋

2𝑌

PRACTICE: Find length

13

𝑆

𝑄

𝑃

𝑥𝑅

7

15

PRACTICE: Use the diagram to find the value of each variable.

PRACTICE: Use the diagram to find the value of each variable.

HOMEWORK #6:

Pg. 400: 3-11, 13-17

If finished, work on other assignments:

HW #1 Pg. 360: 20-52 evenHW #2: Pg. 367: 3-12, 16-18HW #3: Pg. 376: 3-12, 23HW #4: Pg. 384: 3-14, 21-24, 26 (Graph paper needed)HW #5: Pg. 392: 3-12, 18-23