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Lesson 5.4 Midsegments

Lesson 5.4 Midsegments. HW: Lesson 5.4/1-7, 14-16 Quiz Tomorrow Lessons 5.1 -5.4. Midsegment of a trapezoid – the segment that connects the midpoints of the legs. . Definition. The midsegment of a trapezoid is parallel to each base

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Lesson 5.4 Midsegments

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  1. Lesson 5.4 Midsegments HW: Lesson 5.4/1-7, 14-16 Quiz Tomorrow Lessons 5.1 -5.4

  2. Midsegment of a trapezoid – the segment that connects the midpoints of the legs. Definition

  3. The midsegment of a trapezoid is • parallel to each base • its length is one half the sum of the lengths of the bases (average of the bases) Properties of a Midsegment

  4. Definition The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. B E D C A D and E are midpoints DE is the midsegment

  5. B E D C A Triangle Midsegment Conjecture The midsegment of a triangle is • parallel to the third side • half as long as that side. // x 2x

  6. practice EF = AB + CD 2 EF = 11 + 17 2 F E EF = 28 2 EF = 14 in. Find the length of EF

  7. EF is the midsegment of trap ABCD. • Find the length of AD 22 in. 38 in. 76 = 22 + AD practice 54 in. = AD

  8. practice Find AB, mA, and mC EF = AB + CD 2 17 = AB + 24 2 10 in. = AB <C + < B = 180 <A + < D = 180 m<A = 115˚ m<C =78˚

  9. Finding Lengths In ∆XYZ, M, N and P are the midpoints. The Perimeter of ∆ MNP is 60. Find NP and YZ. Because the perimeter is 60, you can find NP. NP + MN + MP = 60 (Definition of Perimeter) NP = • practice X 14 YZ = 2(MP) YZ =2(24) = 48 24 M P 22 Y N Z

  10. In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU. • practice 16 ft 5 ft PR = ________ TU = ________

  11. In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY. • practice 14 cm 53 cm ZY = ________ MN = ________

  12. In the diagram, ED and DF are midsegments of triangle ABC. Find DF and AB. • practice 5X+2 3X - 4 Base = 2 times the midsegment x = ________ 10 DF = ________ 26 AB = ________ 52

  13. Quick Check: • AB = 10 and CD = 28. Find EB, BC, and AC. Midsegment is ½ the base 10 EB = 14 A B is midpoint of AC BC = 10 E B 28 AB + BC = AC 20 AC = C D

  14. Quick Check: 2. Critical Thinking Find the m<VUZ. Justify your answers. X 65O U Z Y V VU is a midsegment, parallel to YX <YXU and < VUZ are corresponding angles 65O m<VUZ =

  15. practice Find JK and AB JK is a midsegment, ½ the length of the base JK = ½ 10 = 5 AB is 2 times the midsegment AB = 2 (6) = 125

  16. practice a) In XYZ, which segment is parallel to Is Why? Yes ST is a midsegment d) Find YZ and XY YZ = 2(4) = 8 XY = 2(5) = 10

  17. practice are midsegments in XYZ. Find the perimeter of XYZ. Bases are 2 times the measure of their midsegment OR Perimeter of ) 0

  18. practice Given: X, Y, and Z are the midpoints of AB, BC, and AC respectively. AX = 2; XY = 3; BC = 9 Find the perimeter of ABC.

  19. practice x + 2 2 ( x + 20) = x + 2 + 4x + 32 x + 20 2x + 40 = 5x+ 34 40 = 3x + 34 4x + 32 6 = 3x 2 = x

  20. practice Given: DE = x + 2; BC = Find DE x + 2 2(x + 2) = 4(x + 2)= 4x + 8 = x + 19 3x = 11

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