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Bell Ringer

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. =.

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Bell Ringer

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  1. Bell Ringer

  2. Triangle Mid-segments

  3. Midsegment of a triangle • A Midsegmentof a triangle is the segments that connects the midpoints to two sides of a triangle.

  4. Example 1 Find Segment Lengths Find the value of x. SOLUTION Triangle Proportionality Theorem = Substitute 4 for CD, 8 for DB, x for CE, and 12 for EA. x = 12 4·12=8 ·x Cross product property 4 48 = 8x 8 Multiply. 8x 48 CD CE = Divide each side by 8. 8 8 DB EA 6 = x Simplify.

  5. Example 2 Find Segment Lengths Find the value of y. SOLUTION You know that PS = 20 and PT = y. By the Segment Addition Postulate, TS = 20 – y. = Triangle Proportionality Theorem y = 20 – y 3 Substitute 3 for PQ, 9 for QR, y for PT, and (20 – y) for TS. 9 PQ PT Cross product property 3(20 – y)=9 ·y TS QR 60 – 3y = 9y Distributive property

  6. Example 2 Find Segment Lengths 60 – 3y + 3y = 9y + 3y Add 3y to each side. 60 = 12y Simplify. Divide each side by 12. 5 = y Simplify. 12y 60 = 12 12

  7. Example 3 SOLUTION Find and simplify the ratios of the two sides divided by MN. , MN is not parallel to GH. Because ANSWER Determine Parallels Given the diagram, determine whether MN is parallel to GH. = = = = LM LN 8 3 8 3 48 56 3 1 ≠ 1 3 21 16 MG NH

  8. Find Segment Lengths and Determine Parallels Now You Try  Find the value of the variable. 1. 8 10 ANSWER ANSWER 2.

  9. Find Segment Lengths and Determine Parallels Given the diagram, determine whether QR is parallel to ST. Explain. ANSWER || Yes; = so QR ST by the Converse of the Triangle Proportionality Theorem. Now You Try  3. ≠ ANSWER no; 4. 4 6 17 15 12 8 23 21

  10. Example 4 Use the Midsegment Theorem Find the length of QS. 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. QS= PT = (10) = 5 1 1 2 2 The length of QS is 5. ANSWER

  11. Use the Midsegment Theorem Now You Try  Find the value of the variable. 5. 6. 24 8 28 ANSWER ANSWER ANSWER 7. Use the Midsegment Theorem to find the perimeter of ABC.

  12. Now You Try 

  13. Now You Try 

  14. Now You Try 

  15. Now You Try 

  16. Page 390

  17. Complete Pages 390-392 #s 10-28 even only

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