Unit Three Theorems and Corollaries

Question 1

If a line segment bisects the vertex angle of an isosceles triangle, the it is also the ___ and ___ to the base.

Answer 1

altitude; median

Question 2

If the line segment is the altitude of the base of an isosceles triangle, then it is also the ___ to the base and the ____ of the vertex angle.

Answer 2

median; bisector

Question 3

If a line segment is the median to the base of an isosceles triangle, then it is also the ____ to the base and the bisector of the ____ angle.

Answer 3

altitude; vertex

Question 4

If a triangle is equilateral, then it is_____.

Answer 4

Equiangular

Question 5

If a triangle to equiangular, then it is______.

Answer 5

Equilateral

Question 6

If a line segment bisects the ____ angle of an _____ triangle, the it is also the altitude and median to the base.

Answer 6

Vertex; Isosceles

Question 7

If the line segment is the ____ of the base of an isosceles triangle, then it is also the median to the base and the bisector of the _____ angle.

Answer 7

Altitude; vertex

Question 8

If a line segment is the ____ to the base of an isosceles triangle, then it is also the altitude to the base and the ____ of the vertex angle.

Answer 8

Median; Bisector

Question 9

If two lines intersect to form two _____________, then the lines are perpendicular.

Answer 9

Congruent adjacent angles

Question 10

Through a point on the line, there exists _____________ line that is perpendicular to the line.

Answer 10

Exactly one

Question 11

Through a point ____ on a line, there exists ___________ line that is perpendicular to the line.

Answer 11

Not; exactly one

Question 12

The No-Choice Theorem (write this theorem out fully during tests)

Answer 12

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent