congruent segments & midpoint of a segment
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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a.CONGRUENT SEGMENTSb.MIDPOINT OF A SEGMENT
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 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
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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 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/ = 20DE = EF = DF ÷ 2 DE = EF= 20 ÷ 2 = 10
D E F -5 15
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 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 orE = F- FE = 15 – 10 = 5
D E F -5 15
10 10
5
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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 + 28 – 2 = 5x – 2x 6 = 3x 2 = x
D E F 2x + 8 5x +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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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 + 63x – 2x= 6- 2 x = 4
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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 ÷ 2E= 2
D E F -5 9 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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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.