Chapter 4

Question 1

1st true statement

Answer 1

since congruent triangles have same shape, their corresponding angles are congruent

Question 2

2nd true statement

Answer 2

since congruent triangles have the same size, their corresponding sides are congruent

Question 3

congruent triangles

Answer 3

2 triangles are congruent if and only if their vertices can be matched up so that the corresponding parts (angles and sides) of the triangles are congruent

Question 4

common side

Answer 4

a side that shares both congruent figures

Question 5

SSS Postulate

Answer 5

if 3 sides of 1 triangle are congruent to 3 sides of another triangle, then the triangles are congruent

Question 6

SAS Postulate

Answer 6

if 2 sides and the included angle of 1 triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent

Question 7

ASA Postulate

Answer 7

if 2 angles and the included side of 1 triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

Question 8

perpendicular line to a plane

Answer 8

a line and a plane are perpendicular if and only if they intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection

Question 9

legs

Answer 9

congruent sides of an isosceles triangle

Question 10

base

Answer 10

third side of isosceles triangle

Question 11

base angles

Answer 11

angles at the end of the base

Question 12

vertex angle

Answer 12

angle opposite the base in an isosceles triangle

Question 13

the isosceles triangle theorem

Answer 13

if 2 sides of a triangle are congruent, then the angles opposite those sides are congruent

or

base angles of an isosceles triangle are congruent

Question 14

corollary 1

Answer 14

an equilateral triangle is also equiangular

Question 15

corollary 2

Answer 15

an equilateral triangle has three 60 degree angles

Question 16

corollary 3

Answer 16

the bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint

Question 17

theorem 4-2

Answer 17

if 2 angles of a triangle are congruent, then the sides opposite those angles are congruent

Question 18

corollary 4

Answer 18

an equiangular triangle is also equilateral

Question 19

AAS Theorem

Answer 19

if 2 angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent

Question 20

hypotenuse

Answer 20

side opposite the right angle in a right triangle

Question 21

legs

Answer 21

other two sides of a right triangle

Question 22

HL Theorem

Answer 22

if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent

Question 23

median

Answer 23

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

Question 24

altitude

Answer 24

perpendicular segment in a triangle from a vertex to the line that contains the opposite side

Question 25

perpendicular bisector

Answer 25

a line that is perpendicular to the segment at its midpoint

Question 26

theorem 4-5

Answer 26

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

Question 27

theorem 4-6

Answer 27

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

Question 28

distance from a point to a line

Answer 28

length of the perpendicular segment from the point to the line

Question 29

theorem 4-7

Answer 29

if a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle

Question 30

theorem 4-8

Answer 30

if a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle