1. 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 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

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 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

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 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

7. 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

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. 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

11. 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

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. 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.