4.7, 10.3, and 5.1 - 5.3

Question 1

Median of a triangle (DEF)

Answer 1

a segment from a vertex to the midpoint of the opposite side

Question 2

Where does the median lie?

Answer 2

ALWAYS on the INSIDE of a triangle

Question 3

Altitude of a triangle (DEF)

Answer 3

The perpendicular segment from a vertex to the line that contains the opposite side.

(Basically from a vertex and is perpendicular to the opp. side)

Question 4

Where can an altitude lay?

Answer 4

inside or outside the triangle, since it has to be perpendicular to the opp. side, for obtuse and acute triangles it will be on the outside of the triangle

Question 5

Perpendicular Bisector of a segment

Answer 5

A line that is perpendicular to the segment at it’s midpoint

Question 6

If a point lies on the perpendicular bisector of a segment,

Answer 6

Then the point is equidistant from the endpoints of the segment. (HAS A CONVERSE)

Question 7

Distance from a point to a line

Answer 7

the length of the perpendicular segment from the point to the line

Question 8

If a point lies on the bisector of an angle,

Answer 8

Then the point is equidistant from the sides of the angle.
(HAS A CONVERSE)

Question 9

Incenter theorem

Answer 9

The bisectors of the angles of a triangle intersect in a point that is equidistant from the three sides of the triangle

Question 10

Circumcenter theorem

Answer 10

The perpendicular bisectors of the sides of a triangle intersect in a point that is equidistant from the three vertices of a triangle

Question 11

Orthocenter theorem

Answer 11

The lines that contain the altitudes of a triangle intersect in a point

Question 12

Centroid theorem

Answer 12

The medians of a triangle intersect at a point that is two-thirds of the distance from each vertex to the midpoint of the opposite side

Question 13

Centroid theorem 2/3’s rule

Answer 13

Centroid is always located 2/3’s from the first part of a segment, and the end is located 1/3 from that same segment

Question 14

Parallelogram

Answer 14

A quadrilateral w/ both pairs of opp. sides parallel

Question 15

If a quadrilateral is a parallelogram (1)

Answer 15

Then the opp. sides are congruent

Question 16

If a quadrilateral is a parallelogram (2)

Answer 16

Then opp. angles are congruent

Question 17

If a quadrilateral is a parallelogram (3)

Answer 17

Then its diagonals bisect eachother

Question 18

If both pairs of opp. sides of a quad. are congruent,

Answer 18

Then the quad. is a parallelogram

Question 19

If both pairs of opp. angles of a quad. are congruent

Answer 19

Then the quad. is a parallelogram

Question 20

If the diagonals of a quad. bisect each other,

Answer 20

Then the quad. is a parallelogram

Question 21

If one pair of opp. sides of a quad are both congruent and parallel,

Answer 21

Then the quad. is a parallelogram

Question 22

If two lines are parallel

Answer 22

Then all points on one line are equidistant from the other line

Question 23

If 3 parallel lines cut off congruent segments on one transversal,

Answer 23

Then they cut off congruent segments on every transversal

Question 24

A line that contains the midpoint of one side of a triangle and is parallel to another side,

Answer 24

passes through the midpoint of the third side

Question 25

The segment that joins the midpoints of two sides of a triangle is (2 THINGS)

Answer 25

1. parallel to the third side
2. is half as long as the third side