chapter 4

Question 1

CPCTC

Answer 1

corresponding parts of congruent triangles are congruent

Question 2

congruent triangles

Answer 2

two triangles are congruent if there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

Question 3

equilateral triangle

Answer 3

an equilateral triangle has 3 congruent sides.

Question 4

isosceles triangle

Answer 4

an isosceles triangle has at least two congruent sides.

Question 5

scalene triangle

Answer 5

a scalene triangle is a triangle that has no congruent sides.

Question 6

vertex

Answer 6

a vertex of a polygon is a common endpoint of two of it’s sides.

Question 7

Opposite side

Answer 7

(un official. refer to theorems notebook for example and diagram) a side opposite an angle of a triangle. (book says in triangle ABC, side BC is opposite angle A).

Question 8

adjacent sides

Answer 8

in a triangle or other polygon, two sides that share a common vertex are adjacent sides.

Question 9

right triangle

Answer 9

a right triangle is a triangle with exactly 1 right angle

Question 10

legs of a right triangle

Answer 10

In a right triangle, the sides adjacent to the right angle are the legs of the triangle.

Question 11

hypotenuse

Answer 11

in a right triangle, the side opposite the right angle is the hypotenuse.

Question 12

acute triangle

Answer 12

an acute triangle has three acute angles.

Question 13

equiangular triangle

Answer 13

an equiangular triangle has three congruent angles, each with a measure of 60°

Question 14

obtuse triangle

Answer 14

an obtuse triangle has exactly one obtuse angle.

Question 15

legs of an isosceles triangle

Answer 15

In an isosceles triangle with 2 congruent sides, the congruent sides are called legs.

Question 16

base of an isosceles triangle

Answer 16

In an isosceles triangle with 2 congruent sides, the third side is called the base of the isosceles triangle.

Question 17

properties of congruent triangles

Answer 17

1. every triangle is congruent to itself
2. If triangle ABC is congruent to triangle PQR, then triangle PQR is congruent to triangle ABC
3. If triangle ABC is congruent to triangle PQR and triangle PQR is congruent to triangle TUV, then triangle ABC is congruent to triangle TUV

Question 18

Interior angles of a triangle

Answer 18

the original three angles in a triangle.

Question 19

exterior angles of a triangle

Answer 19

when the sides of a triangle are extended, the angles that are adjacent to the interior angles of a triangle are the exterior angles. each vertex has a pair of exterior angles

Question 20

triangle sum theorem

Answer 20

the sum of the measures of the interior angles of a triangle is 180°

Question 21

third angles theorem

Answer 21

if 2 angles of 1 triangle are congruent to 2 angles of a second triangle, then the third angles are also congruent.

Question 22

theorem 4.4

Answer 22

the acute angles of a right triangle are complementary

Question 23

exterior angles theorem

Answer 23

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

Question 24

exterior angles inequality theorem

Answer 24

the measure of an exterior angle of a triangle is greater than the measure of either of the two remote interior angles.

Question 25

Side-Side-Side congruence postulate

Answer 25

If 3 sides on 1 triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Question 26

Side-angle-side congruence postulate

Answer 26

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

Question 27

Angle side angle congruence postulate

Answer 27

If 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of a 2nd triangle, then the 2 triangles are congruent.

Question 28

Angle Angle side conguence theorem

Answer 28

If 2 angles and a nonincluded side of 1 triangle are congruent to 2 angles and a nonincluded side of a 2nd triangle, then the 2 triangles are congruent.

Question 29

base angles of an isosceles triangle

Answer 29

In an isosceles triangle, the two angles that have the base as a part of one side are the base angles

Question 30

base angles theorem

Answer 30

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

Question 31

base angles converse theorem

Answer 31

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

Question 32

corollary to base angles (and converse) theorem.

Answer 32

If a triangle is equilateral, it is also equiangular, and if a triangle is equiangular, then it is also equilateral

Question 33

hypotenuse leg congruence theorem

Answer 33

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.