Chapter 6: Relationships with Triangles

Points of Concurrency

100

Perpendicular bisectors meet at this point

circumcenter

200

Angle bisectors meet at this point

Incenter

300

Medians meet at this point

Centroid

400

Altitudes meet at this point

Orthocenter

500

These two points of concurrency can possibly be outside the triangle

Circumcenter and orthocenter

Handy Formulas to Know

100

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

200

Slope

Difference of the y's/Difference of the x's

300

Distance formula

Square root of (x₂-x₁)²+(y₂-y₁)²

400

How to find the perpendicular slope when you have the slope of a side

Take the reciprocal and change the sign

500

How to find the y-intercept

Plug in a point the line will go through and solve for b

Midsegment Triangle

100

How many segments (minimum) will have the same length in a triangle that has a midsegment triangle?

3

200

If AB is the midsegment corresponding with EF, and EF is 44 units, how long is AB?

22

300

True or false: Midsegments are never parallel to their corresponding side.

False

400

How many midsegments are there in a triangle?

3

500

What formula is crucial when drawing midsegments?

Midpoint Formula

Inequalities

100

5 inches, 12 inches

7<x<17

200

12 feet, 18 feet

6<x<30

300

2 feet, 40 inches

16<x<64

400

25 meters, 25 meters

0<x<50

500

Can you make a triangle with these side lengths?

28, 17, 46

NO