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Bell Ringer

Bell Ringer. Proportions and Similar Triangles . 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.

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Bell Ringer

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  1. Bell Ringer

  2. Proportions and Similar Triangles

  3. 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 CE 48 CD = Divide each side by 8. 8 EA 8 DB 6 = x Simplify.

  4. 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

  5. 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

  6. 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

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

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

  9. A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

  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. Checkpoint Now You Try  Use the Midsegment Theorem 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. Page 390

  13. Complete Page 390 #s 2-36 even only

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