Unit 4 Geometry

Unit 4 Geometry

Triangle Inequality Theorem

The sum of two sides must be greater than the 3rd side.

Why?

The two sides have to connect ABOVE the 3rd side... and this takes LONGER.

Multiple Choice

Will these three sides form a triangle?

• yes

• no

Multiple Select

Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.

• 4, 4, 4

• 5, 5, 10

• 3, 6, 9

• 5, 7, 11

• 13, 5, 6

Base Angles

In an isosceles triangle the base angles are congruent (equal)

Multiple Choice

Find the value of x

• 41
• 45
• 31
• 98

Perpendicular Bisector Theorem

All points on the perpendicular bisector are equidistant from the endpoints.

Multiple Choice

• JM = 5

• JM = 10

• JM = 12

• JM = 24

Multiple Choice

Name the segment/line/ray shown in the picture.

• Perpendicular Bisector

• Angle Bisector

• Median

• Altitude

Angle Bisectors

A line that splits an angle into two equal angles

Multiple Choice

Find the measure of  $\angle NJZ$  

• 38

• 90

• 52

• 128

Multiple Choice

Name the segment/line/ray shown in the picture.

• Perpendicular Bisector

• Angle Bisector

• Median

• Altitude

Multiple Choice

Find the measure of  $\angle MFZ$  

• 10

• 19

• 21

• 32 $\frac{1}{3}$  

<ABD = <ABC+<BCD

The two angles add up to make the big angle.

Multiple Choice

Find the value of ∠A.

• 79 degrees
• 87 degrees
• 90 degrees
• 97 degrees

Incenter

The point created by the angle bisectors of a triangle that is equally distant from all 3 sides.

Multiple Choice

Name the point of concurrency shown.

• circumcenter

• incenter

• centroid

• orthocenter

Circumcenter

The intersection of the perpendicular bisectors of a triangle

Multiple Choice

Name the point of concurrency shown.

• circumcenter

• incenter

• centroid

• orthocenter

Median of a Triangle

Median = middle. Connects a vertex of a triangle with the midpoint of the opposite side.

Multiple Choice

Find NM

• 12

• 17

• 31

• 20

Multiple Choice

Identify the special segment that's pictured: 

• Altitude
• Midsegment
• Median
• Angle Bisector

Centroid

The point formed by the 3 medians of a triangle

Multiple Choice

Which of the following words describes the point shown in the figure?

• A. Centerpoint
• B. Orthocenter
• C. Centroid
• D. Midpoint

Altitude of a Triangle

The line perpendicular from a point on a triangle to the opposite side.

Multiple Choice

Name the segment/line/ray shown in the picture.

• Perpendicular Bisector

• Angle Bisector

• Median

• Altitude

Multiple Choice

10. What type of lines are shown

• perpendicular bisectors
• medians
• altitudes
• angle bisectors

Multiple Choice

13. Which line is an altitude?

• XY

• BY

• AZ

• XC

Multiple Choice

Select the triangle that shows the height that goes with the base shown here.

Orthocenter

Where the ALTITUDES intersect

Try it!

Multiple Choice

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

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

Does a triangle with these side lengths exist?
15, 12, 9

• Yes
• No
• I don't know.

Multiple Choice

The figures above are examples of ...

• altitudes

• perpendicular bisectors

• medians

• angle bisectors

Multiple Choice

Point A is the incenter of  $\Delta PQR$ . Find each measure of  $\angle YLA$  

• 21

• 32

• 37

• 58

Multiple Choice

A segment joining a vertex to the opposite side so that is perpendiuclar to that side.

• perpendicular bisector

• angle bisector

• median

• altitude

Multiple Choice

The altitudes of a triangle intersect at the _________________________.

• Centriod
• Circumcenter
• Incenter
• Orthocenter

Multiple Choice

The ORTHOCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Multiple Choice

Can the sides of a triangle have lengths 3, 8, and 9?

• Yes
• No

Multiple Choice

SCULPTURE A triangular entrance way has walls with corner angles of 50°, 70°, and 60°. The designer wants to place a tall bronze sculpture on a round pedestal in a central location equidistant from the three walls. How can the designer find where to place the sculpture?

• Find the circumcenter, where the three perpendicular bisectors meet.

• Find the incenter, where the three angle bisectors meet.

• Draw the perpendicular bisector of the longest side.

• Draw the angle bisector of the greatest angle.