Chapter 4

Question 1

Triangle

Answer 1

a figure formed by three segments joining three noncollinear points.

Question 2

Classification of triangles by sides

Answer 2

Equilateral triangle: 3 congruent sides
Isosceles triangle: at least 2 congruent sides
Scalene Triangle: no congruent sides

Question 3

Classification of triangles by angles

Answer 3

Equinagular triangle: 3 congruent angles
Acute triangle: 3 acute sides
Right triangle: 1 right angle
Obtuse triangle: 1 obtuse angle

Question 4

Theorem 4.1 “Triangle sum theorem”

Answer 4

The sum of the measure of the angles of a triangle is 180`

Question 5

Corollary

Answer 5

a statement that can be proved easily using the theorem

Question 6

Corollary to the triangle sum theorem

Answer 6

The acute angles of a right triangle are complementary

Question 7

Exterior angles

Answer 7

the angles that are adjacent to the interior angles

Question 8

Theorem 4.2 “Exterior angle Theorem”

Answer 8

The measure of an exterior angle of a triangle is equal to the sum of the measure of the two nonadjacent interior angles

Question 9

legs

Answer 9

the congruent sides of an isosceles triangle

Question 10

base

Answer 10

the non congruent leg of a isosceles triangle

Question 11

base angles

Answer 11

the two angles at the base of the triangle

Question 12

Theorem 4.3 “Base Angles Theorem”

Answer 12

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

Question 13

Theorem 4.4 “Converse of the Base angles theorem”

Answer 13

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

Question 14

Theorems 4.5 and 4.6
“Equilateral Theorem”
“Equiangular Theorem”

Answer 14

If a triangle is equilateral, then it is equiangular.

If a triangle is equiangular, then its equilateral.

Question 15

Constructing an equilateral triangle

Answer 15

Draw A-B. Draw an arc with center A that passes through B
Draw an arc with center B that passes through A
The intersection of the arcs is point C.

Question 16

Hypotenuse

Answer 16

the side opposite the right angle

Question 17

Theorem 4.7 “The Pythagorean theorem”

Answer 17

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the square of the length of the legs.
(hypotenuse)^2 = (leg)^2 + (leg)^2

Question 18

Distance formula

Answer 18

AB = ⅆ=√((x_2−x_1 )^2+(y_2−y_1 )^2 )

Question 19

Theorem 4.8 “The converse of the Pythagorean theorem”

Answer 19

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Question 20

If c^2

Answer 20

then the triangle is acute

Question 21

If c^2 = a^2 + b^2

Answer 21

then the triangle is right

Question 22

If c^2 > a^2 + b^2

Answer 22

then the triangle is obtuse

Question 23

median of a triangle

Answer 23

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

Question 24

centroid

Answer 24

the three medians of a triangle intersect at this point

Question 25

Theorem 4.9 “Intersection of Medians of a triangle”

Answer 25

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

Question 26

Theorems 4.10 and 4.11

“triangle inequalities”

Answer 26

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Question 27

Theorem 4.12 “sides of a triangle” (sort of)

Answer 27

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