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**CONGRUENT SEGMENTS & MIDPOINT OF A SEGMENT**

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**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

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**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.

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**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 Find the distance of DF, then DIVIDE the result by 2. The quotient would be the distance of DE & FE. STEP 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

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**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 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 10 10

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**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 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 = or E = F- FE = 15 – 10 = 5 D E F 10 10 5

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**A. Answer the following. 2x + 8 = 5x + 2 8 – 2 = 5x – 2x 6 = 3x 2 = x**

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 x +2

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**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

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**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

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**3x – 2x= 6- 2 x = 4 B. Answer the following. 3x + 2 = 2x + 6**

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

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**B. Answer the following. = 4 ÷ 2 E= 2 E = (D + F) ÷ 2 = (-5 + 9) ÷ 2**

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 2

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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 = ______

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**Write your answers in a one-half crosswise paper.**

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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Midpoint and Distance Formulas

Midpoint and Distance Formulas

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