16.1 Segment Length and Midpoints

16.1 Segment Length and Midpoints

Basic Geometric Terms

In geometry, some of the names of figures and other terms will already be familiar from everyday life. For example, a ray like a beam of light from a spotlight is both a familiar word and a geometric figure with a mathematical definition.

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The most basic figures in geometry are undefined terms, which cannot be defined using other figures. The terms point, line, and plane are undefined terms. Although they do not have formal definitions, they can be described as shown in the table.

Undefined Terms

​In geometry, the word between is another undefined term, but its meaning is understood from its use in everyday language. You can use undefined terms as building blocks to write definitions for defined terms.

Defined Terms

Constructing a Copy of a Line Segment

​Points that lie in the same plane are coplanar. Lines that lie in the same plane but do not intersect are parallel. Points that lie on the same line are collinear. The Segment Addition Postulate is a statement about collinear points. A postulate is a statement that is accepted as true without proof. Like undefined terms, postulates are building blocks of geometry.

Constructing a Copy of a Line Segment

​A construction is a geometric drawing that produces an accurate representation without using numbers or measures. One type of construction uses only a compass and straightedge. You can construct a line segment whose length is equal to that of a given segment using these tools along with the Segment Addition Postulate.

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https://www.youtube.com/watch?v=AFXm-ha6YAY&t=5s

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Practice and Problem Solving A/B #1-2​

Using the Distance Formula on the Coordinate Plane

The Pythagorean Theorem states that a^2+ b^2= c^2, where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse. You can use the Distance Formula to apply the Pythagorean Theorem to find the distance between points on the coordinate plane.

Using the Distance Formula on the Coordinate Plane

​Practice and Problem Solving A/B #3-4

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EF

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GH​

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JK​

Finding a Midpoint

The midpoint of a line segment is the point that divides the segment into two segments that have the same length. A line, ray, or other figure that passes through the midpoint of a segment is a segment bisector.

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You can use the Midpoint Formula to find the midpoint of a segment on the coordinate plane.​

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Practice and

Problem Solving

A/B #5-6

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Multiple Choice

True or False: Points A, B, and C are collinear.

• True
• False

Multiple Choice

True or False: Points B, C, and D are coplanar.

• True
• False

Multiple Choice

A__________ is a fixed position in space and has no dimensions or size.

• Point
• Line
• Plane
• Cube

Multiple Choice

Are points D and E collinear or coplanar?

• Collinear

• Coplanar

• Both

• Neither

Multiple Choice

Given the diagram, which is correct?

• BC+CD=BD

• BD+BC=CD

• CD+BC=BD

• BC+BD=CD

Multiple Choice

Find AC

• 8.5
• 9.5
• 25.5
• 10

Multiple Choice

Given that R is between S and T.
RS=6, TR=4.5, TS= ______

• 1.5
• 10.5
• 6
• 4.5

Multiple Choice

What does the word BISECT mean?

• To cut something into more than five pieces.
• It is a plane with two sets of wings.
• A shape that has three sides. 
• To cut something into two congruent pieces or in half.

Multiple Choice

Find the value of r if M is the midpoint of JK.

• r=64
• r=32
• r=3
• r=1/3

Multiple Choice

RS is the segment bisector.  If OQ = 32 and PO = 4x, what does x equal?

• 8
• 28
• 128
• 36