Unit 4 Geometry

Question 1

Midpoint formula

Answer 1

X one plus x two Y one plus y two
————————. ————————

           2.             ,               2

Question 2

Slope formula

Answer 2

Y one minus y two
—————————-
X one minus X two

Question 3

Distance formula

Answer 3

__________________________________
V ( x one - x two) + ( y one - y two)

Question 4

Midpoint

Answer 4

Connects the midpoints of the sides of a triangle

Question 5

Triangle mid segment theorem

Answer 5

The mid segment of a triangle is parallel to one side of the triangle and half the length

Question 6

Perpendicular bisector theorem

Answer 6

If a point is on the perpendicular bisector line of a triangle then it is equidistant from the endpoint of that segment

Question 7

Perpendicular bisector theorem converse

Answer 7

If a point of equidistant from the endpoints of a segment then it is the perpendicular bisector of that segment

Question 8

Angle bisector theorem

Answer 8

If a point is on the bisector of an angle then it is equidistant from the sides of the angle

Question 9

Angle bisector theorem converse

Answer 9

If a point is equidistant from the sides of and angle then it is on the bisector of the angle

Question 10

Circumcenter

Answer 10

Point equidistant from all angles of a triangle ( can be outside triangle ) found by drawing perpendicular lines

Question 11

Incenter

Answer 11

Point equidistant from all three sides of a triangle found by drawing lines from angle bisectors

Question 12

Centroid

Answer 12

The center of gravity for a triangle also the point where all three medians meet.

Question 13

Medians

Answer 13

Create the centroid and are are 2/3 of length on one side and 1/3 of length on other side . Also are bisector pf the lines they touch

Question 14

Altitudes

Answer 14

Perpendicular segment from a vertex of the triangle to the line containing the opposite side also called the height . ( can be inside or outside the triangle )

Question 15

Orthocenter

Answer 15

The point where 3 altitudes meet can be inside or outside the triangle

Question 16

All triangle similarity postulates

Answer 16

AA
SAS
SSS or Ab ac bc
__=__=__
QR QS RS

Question 17

What is needed for simularity

Answer 17

Same shape but not same size
So same angle measure but not same side length necessarily

Question 18

Side splitter theorem

Answer 18

If a line is parallel to a side of a triangle and cuts through the triangle then it cuts the sides proportionally

Question 19

Side splitter theorem corollary

Answer 19

If multiple parallel lines intersect two transversals then the segments intercepted on the transversals are proportional

Question 20

Triangle angle bisector theorem

Answer 20

The angle bisector of a triangle cut the opposite side into pieces that are proportional to the sides of the angle

Question 21

Perpendicular bisector

Answer 21

A perpendicular line that splits a segment in half

Question 22

Angle bisector

Answer 22

A line the splits an angle in half