Chapter 4: Theorems And Postulates

Question 0

Corollary of Triangle Sum Theorem (right triangles)

Answer 0

The acute angles if a right triangle ate complementary

Question 1

Triangle sum theorem

Answer 1

The sum of the angle measures of a triangle is 180 degrees

Question 2

Corollary of the Triangle sum theorem (equilateral triangles)

Answer 2

The measure if each angle if an equiangular triangle is 60 degrees

Question 3

Exterior angle theorem

Answer 3

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles

Question 4

If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent

Answer 4

Third angles theorem

Question 5

If three sides of one triangle are congruent to three sides if another triangle, then the triangles are congruent

Answer 5

SSS (Side side side congruence postulate)

Question 6

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Answer 6

SAS (Side Angle Side Congruence Postulate)

Question 7

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

Answer 7

ASA (angle side angle triangle congruence postulate)

Question 8

If two angles and the included side of one triangle Rare congruent to the corresponding angles Nc the nonincluded side of another triangle, then the triangles are congruent.

Answer 8

AAS (angle angle side triangle congruence postulate)

Question 9

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent

Answer 9

HL (hypotenuse leg triangle congruence postulate)

Question 10

If two sides of a triangle are congruent, then the angles opposite the sides are congruent

Answer 10

Isosceles Triangle Theorem

Question 11

If two angles of a triangle are congruent, then the sides opposite the sides are congruent

Answer 11

Converse of the isosceles triangle theorem

Question 12

Corollary of the isosceles triangle theorem (equilateral)

Answer 12

If a triangle is equilateral, then it is equiangular

Question 13

Corollary of the isosceles triangle theorem (equiangular)

Answer 13

Equiangular triangles are equilateral

Question 14

If a point is on the perpendicular bisector of a segment, then it is equidistant From the endpoints of the segment

Answer 14

Perpendicular bisector segment

Question 15

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

Answer 15

Converse of the perpendicular bisector theorem

Question 16

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

Answer 16

Angle bisector theorem

Question 17

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

Answer 17

Converse of the angle bisector theorem

Question 18

The circumcenter of a triangle is equidistant from the vertices of the triangle

Answer 18

Circumcenter theorem

Question 19

The Incenter of a triangle is equidistant from the sides of the triangle

Answer 19

Incenter theorem

Question 20

The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint if the opposite side

Answer 20

Centroid theorem

Question 21

A midsegment of a triangle is parallel to a side of a triangle, and it’s length is half the length of that side

Answer 21

Triangle midsegment theorem

Question 22

If two sides of a triangle are not congruent, then the larger angle is opposite the longer side

Answer 22

Thm: in triangle larger angle opposite larger side

Question 23

If two angles of a triangle are not congruent, then the longer side is opposite the larger angle

Answer 23

Thm: in triangle larger side is opposite larger angle

Question 24

The sum of any two side-lengths of a triangle is greater than the third side-length

Answer 24

Triangle inequality theorem

Question 25

If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included angle

Answer 25

Hinge theorem

Question 26

If two sides of one triangle are congruent to two sides of another triangle and the third sides are it congruent, then the larger included angle is across from the longer third side

Answer 26

Converse of the hinge theorem