1-5 Congruent Segments

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Congruent Segments You will learn to identify congruent segments and find the midpoints of segments. What You'll Learn

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Congruent Segments In geometry, two segments with the same length are called ________ _________ You will learn to identify congruent segments and find the midpoints of segments. What You'll Learn

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Congruent Segments In geometry, two segments with the same length are called ________ _________ congruent segments You will learn to identify congruent segments and find the midpoints of segments. What You'll Learn

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Congruent Segments In geometry, two segments with the same length are called ________ _________ congruent segments You will learn to identify congruent segments and find the midpoints of segments. What You'll Learn Definition of Congruent Segments Two segments are congruent if and only if ________________________

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Congruent Segments In geometry, two segments with the same length are called ________ _________ congruent segments You will learn to identify congruent segments and find the midpoints of segments. What You'll Learn Definition of Congruent Segments Two segments are congruent if and only if ________________________ they have the same length

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Congruent Segments B A C R S P Q

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Congruent Segments B A C R S P Q

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Congruent Segments B A C R S P Q

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Congruent Segments x 11 -5 -3 -1 1 3 5 7 9 -6 -4 0 4 8 2 10 6 -2 R S T Y Use the number line to determine if the statement is True or False. Explain you reasoning. Because RS = 4 and TY = 5,

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Congruent Segments There is a unique point on every segment called the _______.

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Congruent Segments There is a unique point on every segment called the _______. midpoint

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Congruent Segments There is a unique point on every segment called the _______. midpoint On the number line below, M is the midpoint of . x 11 -5 -3 -1 1 3 5 7 9 -6 -4 0 4 8 2 10 6 -2 S M T What do you notice about SM and MT ?

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Congruent Segments There is a unique point on every segment called the _______. midpoint On the number line below, M is the midpoint of . x 11 -5 -3 -1 1 3 5 7 9 -6 -4 0 4 8 2 10 6 -2 S M T What do you notice about SM and MT ?

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Congruent Segments There is a unique point on every segment called the _______. midpoint On the number line below, M is the midpoint of . x 11 -5 -3 -1 1 3 5 7 9 -6 -4 0 4 8 2 10 6 -2 S M T What do you notice about SM and MT ? SM = MT

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Congruent Segments Definition of Midpoint A point M is the midpoint of a segment if and only if M is between S and T and SM = MT

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Congruent Segments Definition of Midpoint A point M is the midpoint of a segment if and only if M is between S and T and SM = MT M S T SM = MT

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Congruent Segments Definition of Midpoint A point M is the midpoint of a segment if and only if M is between S and T and SM = MT M S T SM = MT The midpoint of a segment separates the segment into two segments of _____ _____.

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Congruent Segments Definition of Midpoint A point M is the midpoint of a segment if and only if M is between S and T and SM = MT M S T SM = MT The midpoint of a segment separates the segment into two segments of _____ _____. equal length

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Congruent Segments Definition of Midpoint A point M is the midpoint of a segment if and only if M is between S and T and SM = MT M S T SM = MT The midpoint of a segment separates the segment into two segments of _____ _____. equal length So, by the definition of congruent segments, the two segments are _________.

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Congruent Segments Definition of Midpoint A point M is the midpoint of a segment if and only if M is between S and T and SM = MT M S T SM = MT The midpoint of a segment separates the segment into two segments of _____ _____. equal length So, by the definition of congruent segments, the two segments are _________. congruent

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A Since B is the midpoint: AB = BC

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A Since B is the midpoint: AB = BC Write the equation involving x : 5x – 6 = 2x

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A Since B is the midpoint: AB = BC Write the equation involving x : 5x – 6 = 2x Solve for x : 5x – 2x – 6 = 2x – 2x

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A Since B is the midpoint: AB = BC Write the equation involving x : 5x – 6 = 2x Solve for x : 5x – 2x – 6 = 2x – 2x 3x – 6 + 6 = 0 + 6 3x = 6

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A Since B is the midpoint: AB = BC Write the equation involving x : 5x – 6 = 2x Solve for x : 5x – 2x – 6 = 2x – 2x 3x – 6 + 6 = 0 + 6 3x = 6 x = 2

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A Since B is the midpoint: AB = BC Write the equation involving x : 5x – 6 = 2x Solve for x : 5x – 2x – 6 = 2x – 2x 3x – 6 + 6 = 0 + 6 3x = 6 x = 2 AB = 5x – 6 = 5(2) – 6 = 10 – 6 = 4 Check!

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Congruent Segments In the figure, B is the midpoint of . Find the value of x. 5x - 6 2x C B A Since B is the midpoint: AB = BC Write the equation involving x : 5x – 6 = 2x Solve for x : 5x – 2x – 6 = 2x – 2x 3x – 6 + 6 = 0 + 6 3x = 6 x = 2 AB = 5x – 6 = 5(2) – 6 = 10 – 6 = 4 BC = 2x = 2(2) = 4 Check!

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Congruent Segments To bisect something means to separate it into ___ congruent parts.

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two The ________ of a segment bisects the segment because it separates the segment into two congruent segments.

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two The ________ of a segment bisects the segment because it separates the segment into two congruent segments. midpoint

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two The ________ of a segment bisects the segment because it separates the segment into two congruent segments. A point, line, ray, or plane can also bisect a segment. midpoint B A E G C D

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two The ________ of a segment bisects the segment because it separates the segment into two congruent segments. A point, line, ray, or plane can also bisect a segment. midpoint B A E G C D

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two The ________ of a segment bisects the segment because it separates the segment into two congruent segments. A point, line, ray, or plane can also bisect a segment. midpoint B A E G C D

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two The ________ of a segment bisects the segment because it separates the segment into two congruent segments. A point, line, ray, or plane can also bisect a segment. midpoint B A E G C D

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Congruent Segments To bisect something means to separate it into ___ congruent parts. two The ________ of a segment bisects the segment because it separates the segment into two congruent segments. A point, line, ray, or plane can also bisect a segment. midpoint B A E G C D