Midpoints and Angle Bisectors

Geometry Section 5.3

Concurrent Lines, Perpendicular Bisectors and Angle Bisectors

Multiple Choice

What is the property of a point on the perpendicular bisector of a segment.

• It is equidistant from the sides of the angle.

• It is equidistant from the endpoints of the segment

• It is equally distant from the sides of the triangle

• It is what it is.

Multiple Choice

What is the property of a point on the angle bisector of an angle.

• It is equidistant from the sides of the angle.

• It is equidistant from the endpoints of the segment

• It is equally distant from the vertices of the triangle

• It is what it is.

Multiple Choice

14. Which line is a perpendicular bisector?

• XY
• BY
• AZ
• XC

​Concurrent Lines

• ​Three or more lines that intersect at exactly one point.

• ​

• ​Point of concurrency - the point of intersection of three or more lines.

Multiple Choice

What is this line an example of?

• perpendicular bisector

• angle bisector

• median

• altitude

​What is a CIRCUMCENTER?

The point of concurrency created by the 3 perpendicular bisectors.

​

​Notice: Each vertex of the triangle is EQUIDISTANT from the circumcenter.

​

Why is that?! They are the RADIUS of the outside circle!

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Multiple Choice

The CIRCUMCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Multiple Choice

What is the ray and example of?

• perpendicular bisector

• angle bisector

• median

• altitude

​What is an INCENTER?

​

The point of concurrency created by the 3 angle bisectors.

​​

​They all meet at the INCENTER.

​

The Incenter is EQUIDISTANT from the sides of the Triangle

​

​Notice: The circle is INside.

Multiple Choice

The INCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

​Incenter

​The point of concurrency of the angle bisectors.

​

​Equidistant from the sides of the triangle.

​

​https://www.geogebra.org/m/YZtmbSx8

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Multiple Choice

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

[Angle Bisectors and Incenter]:
If PX is 5, what is PZ?

• 20
• 10
• 5
• 15

Multiple Choice

The incenter of a triangle is equidistant from the __________ of a triangle.

• vertices
• sides
• angle bisector
• circumcenter

Multiple Choice

[Perpendicular Bisectors and Circumcenter]
If AF is 6, what is AC?

• 6
• 10
• 16
• 12

Multiple Choice

If S is the incenter, what type of segments are drawn?

• medians
• angle bisectors
• perpendicular bisectors
• altitudes

Multiple Choice

Find the value of x

• x=28
• x=14
• x=23
• x=46

Multiple Choice

The circumcenter is _________________ in the triangle.  

• always
• sometimes
• never
• definitely

Multiple Choice

Point O is the circumcenter of the triangle. Find OB

• OB = 4
• OB = 6
• OB = 5.1
• Not enough information

Multiple Choice

The circumcenter of a triangle is equidistant from the _______ of the triangle.

• vertices
• sides
• center
• midsegment

Multiple Choice

Find the length of AD

• 2
• 4
• 6
• 8

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

What does point O represent in the picture?

• Centroid

• Circumcenter

• Incenter

• Orthocenter

Multiple Choice

Which point is equidistant from the vertices?

• Circumcenter
• Incenter
• Neither
• Bilateral

Multiple Choice

Point P is the circumcenter, which segment is equal to PB

• DA
• AC
• PC
• PF

Multiple Choice

P is the incenter of triangle JKL. Find OP.

• 8

• 13

• 17

• 4

​Homework

​Worksheet/Notesheet - Formative 5.3

Day 1
1, 2, 5, 6, 8, 10, 12, 14, 16

Day 2
3, 4, 7, 9 - 17 odd, 18, 19, 20

​Homework

​Worksheet/Notesheet

Day 1
11 - 18, 19 - 29 odd

Day 2
#20 - 30 even, 31 - 38