Triangle Segments and Centers

Triangle Segments and Centers

There are four different segments that can be created in triangles and their intersection is a measure of center.

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Triangle Segments and Concurrency

​There are multiple ways to bisect triangle sides.

Each type of bisecting segment has a name.

Where the three segments connect, you have a point of concurrency.

Each of the different points of concurrency has a name.​

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Multiple Choice

3 or more lines that intersect at the same point

• Concurrent Lines
• Congruent Lines
• Perpendicular Lines
• Parallel Lines

Perpendicular Bisectors always cross a line segment at right angles, cutting it into two equal parts.

​Some text here about the topic of discussion.

​Perpendicular Bisector

Multiple Choice

Which line is a perpendicular bisector for this triangle?

• Line CF

• Line BG

• Segment ED

• Segment AB

In a triangle, there are three perpendicular bisectors that all meet in one point, the circumcenter.

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The circumcenter can be inside or outside the triangle.​

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​Circumcenter

Multiple Choice

Define: CIRCUMCENTER OF A TRIANGLE

• the intersection point of the three perpendicular bisectors of a triangle 
• when a circle passes through the three vertices of a triangle 
• the point of intersection of three or more lines 
• the intersection point of the three angle bisectors of a triangle 

The bisector of an angle cuts the angle in half exactly.

​Angle Bisector

Multiple Choice

Which line is an angle bisector for this triangle?

• Line CF

• Line BG

• Segment ED

• Segment AB

The angle bisectors of the three interior angles all meet at one point at the center of the triangle, called the incenter.

​Incenter

Multiple Choice

Define: INCENTER OF A TRIANGLE

• the intersection point of the three angle bisectors of a triangle 
• when three or more lines intersect at a single point 
• the intersection point of the three perpendicular bisectors of a triangle 
• the point of intersection of three or more lines 

A median of a triangle is a line from a vertex to the midpoint of the opposite side.

​Median

Multiple Choice

Which line is a median for this triangle?

• Line CF

• Line BG

• Segment ED

• Segment AB

Every triangle has three medians which meet at a point called the centroid.​

Centroid

Multiple Choice

The centroid is the point of concurrency of the 3 ____ of a triangle. 

• Medians
• Midsegments
• Perpendicular Bisectors
• Angle Bisectos

The altitude of a triangle is the line segment from a vertex to the opposite side, and perpendicular to that side.

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An altitude can be outside or inside the triangle.​

Altitude

Multiple Choice

Which line is an altitude for this triangle?

• Line CF

• Line BG

• Segment ED

• Segment AB

The point where the altitudes of a triangle meet is the orthocenter.

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The orthocenter can be outside or inside the triangle.​

Orthocenter

Multiple Choice

The ORTHOCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Summary

Multiple Choice

The figure is an example of a(n) ...

• angle bisector
• perpendicular bisector
• median
• midsegment

Multiple Choice

The figure is an example of a(n) ...

• altitude 
• perpendicular bisector
• midsegment
• angle bisector

Multiple Choice

The figure is an example of a(n) ...

• angle bisector
• midsegment
• altitude
• median

Multiple Choice

Is segment AB a median, altitude, neither or both?

• median

• altitude

• neither

• both

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

Name the point of concurrency shown.

• circumcenter

• incenter

• centroid

• orthocenter

Multiple Choice

Which of the following points is the BALANCE POINT of a triangle. The correct method is shown in the triangle if you look at the markings.

• A. Circumcenter

• B. Orthocenter

• C. Centroid

• D. Midpoint

Multiple Choice

What is the only special triangle segment that does not have to go through a vertex?

• Median

• Altitude

• Angle Bisector

• Perpendicular Bisector

Multiple Choice

Which center points of a triangle are always inside the triangle?

• Centroid and Circumcenter

• Orthocenter and Incenter

• Incenter and Centroid

• Circumcenter and Incenter

​Review: Triangles

Multiple Choice

Will the side lengths 6, 8, 11 make a triangle?

• Yes

• No

Multiple Choice

Will the side lengths 5, 6, 12 make a triangle?

• Yes

• No

Multiple Choice

What is the measure of ∠A?

• 46

• 134

• 90

• 88

Multiple Choice

What is the measure of ∠S?

• not enough information

• 30

• 60

• 180

Multiple Choice

In an ______________ triangle, all three angles are less than 90 degrees.

• acute

• right

• obtuse

• 360 degrees

Multiple Choice

Which equation below could you use to solve for x?

• 30+x+67=180

• x+67+30=180

• 30+x+67+90=180

• x+67+30=90

Multiple Choice

What are complementary angles?

• Angles that add up to 180°
• Angles that add up to 90°
• Angles that are equal to each other
• Angles that are opposite of each other when lines intersect.