Chapter 5: Congrunce Based On Triangles

Question 0

Altitude of a Triangle

Answer 0

Segment drawn for a vertex to the opposite side of a triangle that creates a perpendicular line

Question 1

Median of a Triangle

Answer 1

Segment that is drawn from a vertex to the midpoint of the opposite side

Question 2

Angle Bisector of a Triangle

Answer 2

Segment drawn that bisects any angle of the triangle

Question 3

Perpendicular Bisector of a line segment

Answer 3

a line that is perpendicular to the line segement at its midpoint

Question 4

Isosceles Triangle Theorem

Answer 4

• If two sides of a triangle are congruent, the angles opposite these sides are congruent
• The median from the vertex angle of an isosceles triangle bisects the vertex angle
• The median from the vertex angle of an isosceles triangle is perpendicular to the base

Question 5

Equilateral Triangle

Answer 5

every equilateral triangle is equiangular

Question 6

Theorems

Answer 6

If two points are each equidistant from the endpoints of a line segment, then the points determine the perpendicular bisector of the line segment

Question 7

Theorems

Answer 7

if a point is equidistant from the endpointd of a line segment, then it is on the perpendocular bisector of the line segment

Question 8

Theorems

Answer 8

if a point on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the line segment

Question 9

Theorems

Answer 9

a point is on the perpendicular bisector of a line segment if and only if it is equidistant from the endpoints of the line segment

Question 10

Methods of Proving Line Segments Perpendicular

Answer 10

1. The two lines form right angles at their point of intersection
2. The two lines form congruent adjacent angles at their point of intersection
3. Each of the two points on one line is equidistant from the endpoints of a segment of the other

Question 11

Concurrent

Answer 11

When three perpendicular bisectors of the sides of a triangle are drawn, they are concurrent (they intersect in one point which is called the circumcenter)

• The perpendicular bisectors of the sides of a triangle are concurrent

Question 12

Construct a line segement congruent to a given line segment

Answer 12

Question 13

Construct an angle congruent to a given angle

Answer 13

Question 14

Construct a perpendicular bisector of a given line segment and the midpoint of a given line segment

Answer 14

Question 15

Bisect a given angle

Answer 15

Question 16

Construct a line perpendicular to a given line through a given point on the line

Answer 16

Question 17

Construct a line perpendicular to a given line through a point not given on the line

Answer 17