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CONGRUENT SEGMENTS & MIDPOINT OF A SEGMENT

CONGRUENT SEGMENTS & MIDPOINT OF A SEGMENT. Congruent segments MIDPOINT OF A SEGMENT. Consider the figure below. If DE = 5 and EF = 5, then what can you say about segment DE and segment EF? A. If DF = 30, DE = x +5 & EF = 2x -2, find the value of x, the length of DE and EF.

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CONGRUENT SEGMENTS & MIDPOINT OF A SEGMENT

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  1. CONGRUENT SEGMENTS & MIDPOINT OF A SEGMENT Congruent segments MIDPOINT OF A SEGMENT

  2. Consider the figure below. • If DE = 5 and EF = 5, then what can you say about segment DE and segment EF? • A. If DF = 30, DE = x +5 & EF = 2x -2, find the value of x, the length of DE and EF. • When can we say that two segments are congruent? D E F

  3. Definition of Congruent segments • “Two segments are said to be congruent if and only if they have the same measure.” There is a phrase “if & only if”which means that the definition is two way. • 1) If the segments are congruent, then they are equal. • 2) If the segments are equal, then they are congruent.

  4. A. Answer the following questions. • 1. D, E & F are the three collinear points. The coordinate of D is -5 and the coordinate of F is 15. What is the coordinate of E if DE = FE? • 6. Given the figure below. • SOLUTION: • STEP 1. Find the distance of DF, then DIVIDE the result by 2. The quotient would be the distance of DE & FE. • STEP 2. To find the coordinate of E , use any of the following method; • 1. ADD the length of DE and the coordinate of D, or • 2. SUBTRACT the coordinate of F and the length of EF. D E F • -5 15

  5. A. Answer the following questions. • 1. D, E & F are the three collinear points. The coordinate of D is -5 and the coordinate of F is 15. What is the coordinate of E if DE = FE? • 6. Given the figure below. • SOLUTION: • STEP 1. Find the distance of DF, then DIVIDE the result by 2. The quotient would be the distance of DE & FE. • DF = /-5 – 15/ = /-20/ = 20 • DE = EF = DF ÷ 2 • DE = EF= 20 ÷ 2 = 10 D E F • -5 15 10 10

  6. A. Answer the following questions. • 1. D, E & F are the three collinear points. The coordinate of D is -5 and the coordinate of F is 15. What is the coordinate of E if DE = FE? • 6. Given the figure below. • STEP 2. To find the coordinate of E , use any of the following method; • 1. ADD the length of DE and the coordinate of D. • 2. SUBTRACT the coordinate of F and the length of EF. • E = DE +D = 10 +(-5)= = 10 – 5 = 5 or • E = F- FE = 15 – 10 = 5 D E F • -5 15 10 10 5

  7. A. Answer the following. • 2. D, E & F are the three collinear points. If DE = FE and DE = 2x + 8, FE = 5x + 2, find x. • 6. Given the figure below. • SOLUTION: • Write an equation for x using definition of congruent segments, then solve. • DE = FE ( GIVEN) • 2x + 8 = 5x + 2 • 8 – 2 = 5x – 2x • 6 = 3x • 2 = x D E F • 2x + 8 5x +2

  8. Consider the figure below. • If DE = 5 and EF = 5, then what can you say about point E? • A. If DF = 30, DE = x +5 & EF = 2x -2, find the value of x, the length of DE and EF. • What is a midpoint of a segment? D E F

  9. Definition of Midpoint of a segment • is a point of the segment which divides the segment into two congruent parts. • In the figure, if Point E is the midpoint of segment DF, then • DE = EF or • DE  EF D E F

  10. B. Answer the following. • 1. If M is the midpoint of A & C, AM= 3x +2 and MC = 2x + 6, find x. • SOLUTION: • Write an equation for x using definition of congruent segments, then solve. • AM = MC ( M is the midpoint of AC) • 3x + 2 = 2x + 6 • 3x – 2x= 6- 2 • x = 4

  11. B. Answer the following. • 2. Find the coordinate of E, if E is the midpoint D and F. • SOLUTION: • E = (D + F) ÷ 2 • = (-5 + 9) ÷ 2 • = 4 ÷ 2 • E= 2 D E F • -5 9 2

  12. TRY THIS OUT….. • 1. A, U and V are points on a line with point U as their midpoint. If AV = 30 and AU = 2x + 5, find: • A. X =_______ • B. AU = ______ • C. UV = ______

  13. ASSIGNMENT • EXERCISES A, PAGE 40 on workbook. • EXERCISES B, NOS. 4 & 5, PAGE 41 on workbook. Write your answers in a one-half crosswise paper.

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