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Bell Ringer. Triangle Mid-segments. Midsegment of a triangle. A Midsegment of a triangle is the segments that connects the midpoints to two sides of a triangle. Example 1. Find Segment Lengths. Find the value of x. SOLUTION. Triangle Proportionality Theorem. =. - PowerPoint PPT Presentation
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Bell Ringer
Triangle Mid-segments
Midsegment of a triangle
• A Midsegment of a triangle is the segments that connects the midpoints to two sides of a triangle.
Example 1 Find Segment Lengths
Find the value of x.
48
x12= Substitute 4 for CD, 8 for DB, x for
CE, and 12 for EA.4 · 12 = 8 · x Cross product property
48 = 8x Multiply.
488 = 8x
8 Divide each side by 8.
SOLUTION
CDDB = CE
EA Triangle Proportionality Theorem
6 = x Simplify.
Example 2 Find Segment Lengths
Find the value of y.
39
y20 – y= Substitute 3 for PQ, 9 for QR, y
for PT, and (20 – y) for TS.
3(20 – y) = 9 · y Cross product property
60 – 3y = 9y Distributive property
PQQR = PT
TS Triangle Proportionality Theorem
SOLUTION
You know that PS = 20 and PT = y. By the Segment Addition Postulate, TS = 20 – y.
Example 2 Find Segment Lengths
6012 = 12y
12 Divide each side by 12.
60 – 3y + 3y = 9y + 3y Add 3y to each side.
60 = 12y Simplify.
5 = y Simplify.
Example 3 Determine Parallels
Given the diagram, determine whether MN is parallel to GH.
SOLUTION
Find and simplify the ratios of the two sides divided by MN.
LMMG = 56
21 = 83
LNNH = 48
16 = 31
ANSWER Because ≠ 31
83
, MN is not parallel to GH.
Now You Try Find Segment Lengths and Determine Parallels
Find the value of the variable.
1.
2.
ANSWER 8
ANSWER 10
Find Segment Lengths and Determine Parallels
4.
3.
Given the diagram, determine whether QR is parallel to ST. Explain.
ANSWER
Converse of the Triangle Proportionality Theorem.
= 612
48Yes; || so QR ST by the
≠ 1723
1521no;ANSWER
Now You Try
Example 4 Use the Midsegment Theorem
Find the length of QS.
12QS = PT = (10) = 51
2
ANSWER The length of QS is 5.
SOLUTION
From the marks on the diagram, you know S is the midpoint of RT, and Q is the midpoint of RP. Therefore, QS is a midsegment of PRT. Use the Midsegment Theorem to write the following equation.
Use the Midsegment Theorem
Find the value of the variable.
ANSWER 8
ANSWER 24
5.
6.ANSWER 28
7. Use the Midsegment Theorem to find the perimeter of ABC.
Now You Try
Now You Try
Now You Try
Now You Try
Now You Try
Page 390
Complete Pages 390-392#s 10-28 even only
