Lesson 5 4 Prove Midsegment Theorem Use Midsegment

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Lesson 5 -4 Prove ∆ Midsegment Theorem Use ∆ Midsegment Theorem

Lesson 5 -4 Prove ∆ Midsegment Theorem Use ∆ Midsegment Theorem

Prove ∆ Midsegment Theorem ∆ Midsegment Thm A Midsegment of a ∆ is parallel

Prove ∆ Midsegment Theorem ∆ Midsegment Thm A Midsegment of a ∆ is parallel to a side of the ∆ and equals half the length of that side. A M N =2● B C

Use ∆ Midsegment Theorem EXAMPLE 1 A M X N Y B B A

Use ∆ Midsegment Theorem EXAMPLE 1 A M X N Y B B A C C

Use ∆ Midsegment Theorem EXAMPLE 2 a) BD = C Find Each measure. AE

Use ∆ Midsegment Theorem EXAMPLE 2 a) BD = C Find Each measure. AE 17 = 8. 5 = 2 2 ∆ Midsegment Thm xo 26 o b) m<CBD = m<BDF = 26 o Alternate interior <s D 6. 2 B A F 17 E

Question 1 Use the diagram for exercises 1 -6 Y Find each measure 1)

Question 1 Use the diagram for exercises 1 -6 Y Find each measure 1) NM = YX 10 2 = 5 10 2 = 2) XZ = 2●ML = 2●(7) = 14 3) NZ = ZX 2 = 14 2 = 7 M 29 o 7 29 o Z 4) m<LMN = m<MNZ = 29 o Alt. int. <s 5) m<YXZ = m<MNZ = 29 o Corresponding. <s 6) m<XLM = 180 o – m<LMN = 180 o – 29 o = L 151 o N X

Question 2 Use the diagram for exercises 7 -12 H Find each measure Q

Question 2 Use the diagram for exercises 7 -12 H Find each measure Q J 55 o 7) GJ = 2●PQ = 2● 19 = 38 19 55 o 27 P 8) RQ = 9) RJ = HG 2 GJ 2 = = 27 2 38 2 = 13. 5 = 19 R G 10) m<PQR = m<QRJ = 55 o Alt. int. <s 11) m<HGJ = m<QRJ = 55 o Corresponding. <s 12) m<GPQ = 180 o – m<PQR = 180 o – 55 o = 125 o Same side. <s

Use ∆ Midsegment Theorem EXAMPLE 3 Find the value of n AE = 2●BD

Use ∆ Midsegment Theorem EXAMPLE 3 Find the value of n AE = 2●BD ∆ Midsegment Thm C 8 n + 10 = 2● 5 n 8 n + 10 = 10 n 10 = 2 n n= 5 B 5 n D 8 n + 10 A E

Question 3 Use the diagrams for exercises 13 -14 Find the value of n

Question 3 Use the diagrams for exercises 13 -14 Find the value of n 14) 13) 3 n n– 9 54 35 2● 3 n = 54 2●(n – 9) = 35 6 n = 54 2 n – 18 = 35 n= 9 2 n = 53 n = 26. 5

Question 4 Use the diagram for exercises 15 -17 H Find each measure 4

Question 4 Use the diagram for exercises 15 -17 H Find each measure 4 15) Find the perimeter of ∆GHJ 12 Perimeter = JH + HG + GJ = 8 7 L K + 12 + 14 = 34 4 4 6 16) Find the perimeter of ∆KLM J Perimeter = LK + KM + ML = 7 + 4 + M 14 G 6 = 17 17) What is the relationship between the two perimeters? The perimeter of ∆GHJ is twice the perimeter of ∆KLM

Question 5 PQ is a Midsegment of ∆RST. What is the length of RT?

Question 5 PQ is a Midsegment of ∆RST. What is the length of RT? S A. 9 C. 45 B. 21 D. 63 P 4 x – 27 = 2●(x + 9) 4 x – 27 = 2 x + 18 x+9 Q 4 x – 27 R 4 x – 2 x = 18 + 27 2 x = 45 x = 22. 5 RT = 4(22. 5) – 27 = 63 T

Question 6 ∆XYZ is the Midsegment triangle of ∆JKL, XY = 8, YK =

Question 6 ∆XYZ is the Midsegment triangle of ∆JKL, XY = 8, YK = 14, and m<YKZ = 67 o. Which of the following CANNOT be determined? J E. KL G. m<XZL 14 F. JY H. m<KZY Y 8 X 14 K 67 o Z 16 L

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5 4 The Triangle Midsegment Theorem Objective Prove5 4 The Triangle Midsegment Theorem Objective Prove
5 4 The Triangle Midsegment Theorem Objective Prove5 4 The Triangle Midsegment Theorem Objective Prove
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5
5 4 Theorem The Triangle Midsegment Theorem 55 4 Theorem The Triangle Midsegment Theorem 5