1. 9.4(b) Notes: Triangle Midsegment Theorem
Date:
9.4(b) Notes: Triangle Midsegment Theorem
Lesson Objective: Use proportional parts within triangles and with parallel lines.
CCSS: G.SRT.4, 5 
You will need: CPR, 3 colored pens 
This is Jeopardy!: This is what the midpoint does to a line segment.

2. Lesson 1: Triangle Midsegment Theorem
Move down the page about 2” (or 8 lines). Use a compass to construct ∆PQR with base PR 3.5” in red, side PQ 2” in blue, and side QR 3” in a third color. Or use a protractor to make m/ P = 57° and m/ R = 35°. Be exact.
57° °
P ” R

3. Lesson 1: Triangle Midsegment Theorem
Construct or use a ruler to find the midpoint of PQ, label it X. Construct the midpoint of QR, label it Y, and construct the midpoint of PR, label it Z. Mark all congruent segments. Q
2” ”
57° °
P ” R

4. • Lesson 1: Triangle Midsegment Theorem
Con­nect X to Y using a red pen, Y to Z us­ing a blue pen and Z to X using the third colored pen. Q
X Y
P Z R •

5. • Lesson 1: Triangle Midsegment Theorem
Trace ∆XYZ onto the tissue paper us­ing the 3 different col­ors. What do you notice when you trans­form ∆XYZ onto the other tri­an­gles? Label con­gru­ent segments. Q
X Y
P Z R •

6. Lesson 1: Q
X Y
P Z R
Triangle Midsegment Theorem: A mid-segment of a Δ is | | to a side of the Δ, and its length is ½ the length of that side. •

7. • Lesson 1: Triangle Midsegment Theorem
Midpoints: X, Y, Z; Midsegments: XY, YZ, XZ
XY | | PR, XY = ½PR or PR = 2XY
YZ | | QP, YZ = ½QP or QP = 2YZ
XZ | | QR, XZ = ½QR or QR = 2XZ Q
X Y
P Z R •

8. Lesson 2: Using the Triangle Midsegment Theorem
Find each measure. DE DB
m/ FED AB

9. Lesson 3:
Congruent Parts of | | Lines:

10. Lesson 4:
Find x. Then find the side lengths.
A B.

11. 9.4(b): Do I Get It? Yes or No XZ ST
m/ RYX

12. 9.4(a): Do I Get It? Continued
4. Find x and y.