You will learn to identify congruent segments and find the midpoints of segments.

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Reflexive example: AB = AB Symmetric example: AB = BA

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Presentation transcript:

You will learn to identify congruent segments and find the midpoints of segments.

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

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. Definition of Congruent Segments Two segments are congruent if and only if ________________________

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. Definition of Congruent Segments Two segments are congruent if and only if ________________________ they have the same length

B A C R S P Q

B A C R S P Q

B A C R S P Q

x R STY Use the number line to determine if the statement is True or False. Explain you reasoning.

x R STY Use the number line to determine if the statement is True or False. Explain you reasoning. Because RS = 4 and TY = 5,

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________.

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems Theorems are statements that can be justified by using logical reasoning.

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems Theorems are statements that can be justified by using logical reasoning. 2 – 1 Congruence of segments is reflexive.

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems Theorems are statements that can be justified by using logical reasoning. 2 – 1 Congruence of segments is reflexive.

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems Theorems are statements that can be justified by using logical reasoning. 2 – 1 Congruence of segments is reflexive. 2 – 2 Congruence of segments is symmetric.

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems Theorems are statements that can be justified by using logical reasoning. 2 – 1 Congruence of segments is reflexive. 2 – 2 Congruence of segments is symmetric.

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems Theorems are statements that can be justified by using logical reasoning. 2 – 1 Congruence of segments is reflexive. 2 – 2 Congruence of segments is symmetric. 2 – 3 Congruence of segments is transitive.

Since congruence is related to the equality of segment measures, there are properties of congruence that are similar to the corresponding properties of equality. These statements are called ________. theorems Theorems are statements that can be justified by using logical reasoning. 2 – 1 Congruence of segments is reflexive. 2 – 2 Congruence of segments is symmetric. 2 – 3 Congruence of segments is transitive.

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

midpoint

There is a unique point on every segment called the _______. midpoint On the number line below, M is the midpoint of. x SMT What do you notice about SM and MT?

There is a unique point on every segment called the _______. midpoint On the number line below, M is the midpoint of. x SMT What do you notice about SM and MT?

There is a unique point on every segment called the _______. midpoint On the number line below, M is the midpoint of. x SMT What do you notice about SM and MT? SM = MT

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

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

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 _____ _____.

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

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 _________.

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

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

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

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

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

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 – = x = 6

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 – = x = 6 x = 2

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 – = x = 6 x = 2 AB = 5x – 6 = 5(2) – 6 = 10 – 6 = 4 Check!

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 – = x = 6 x = 2 AB = 5x – 6 = 5(2) – 6 = 10 – 6 = 4 BC = 2x = 2(2) = 4 Check!

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

two

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.

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

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

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

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

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

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