Chapter 4 Overview

Question 1

congruent figures

Answer 1

have the same size and shape; you can slide, flip, or turn

one so that it fits exactly on the other one

Question 2

congruent polygons

Answer 2

have congruent corresponding parts – their matching
sides and angles

*When you name congruent polygons, you must list corresponding vertices in
the same order.

Question 3

Theorem 4-1 – Third Angles Theorem

Answer 3

If 2 angles of one ∆ are ≅ to 2 ∠’s of another ∆, then the third ∠’s are ≅.

Question 4

Postulate 4-1 – Side-Side-Side (SSS) Postulate

Answer 4

If the three sides of one ∆ are ≅ to the three sides of another ∆, then the 2
∆’s are ≅.

Question 5

Postulate 4-2 – Side-Angle-Side (SAS) Postulate

Answer 5

If 2 sides and the include angle of one ∆ are ≅ to 2 sides and the included ∠
of another ∆, then the 2 ∆’s are ≅.

Question 6

included angle

Answer 6

he angle between two sides of a triangle

Question 7

included side

Answer 7

The common leg of two angles

Question 8

Postulate 4-3 – Angle-Side-Angle (ASA) Postulate

Answer 8

If 2 ∠’s and the included side of one ∆ are ≅ to 2 ∠’s and the included side of
another ∆, then the 2 ∆’s are ≅.

Question 9

Theorem 4-2 – Angle-Angle-Side (AAS) Theorem

Answer 9

If 2 ∠’s and a nonincluded side of one ∆ are ≅ to 2 ∠’s and
the corresponding nonincluded side of another
triangle, then the ∆’s are ≅.

Question 10

CPCTC

Answer 10

If you know 2 triangles are congruent, then you know that every pair of their
corresponding parts is also congruent.

Question 11

Isosceles triangle

Answer 11

triangle that has 2 sides of equal length

Question 12

vertex angle

Answer 12

angle formed by the 2 ≅ legs

Question 13

base angles

Answer 13

other 2 angles

Question 14

legs

Answer 14

congruent sides of an isosceles triangle

Question 15

base

Answer 15

the side not ≅ to another side

Question 16

Theorem 4-3 – Isosceles Triangle Theorem

Answer 16

If 2 sides of a ∆ are ≅, then the ∠’s opposite those sides are ≅.

Question 17

Theorem 4-4 – Converse of the Isosceles Triangle Theorem

Answer 17

If 2 ∠’s of a ∆ are ≅, then the sides opposite those ∠’s are ≅.

Question 18

Theorem 4-5

Answer 18

If a line bisects the vertex ∠ of an isosceles ∆, then the line is also the
perpendicular bisector of the base.

Question 19

corollary

Answer 19

theorem that can be proved easily using another theorem

Question 20

Corollary to Theorem 4-3

Answer 20

If a ∆ is equilateral, then the ∆ is equiangular.

Question 21

Corollary to Theorem 4-4

Answer 21

If a ∆ is equiangular, then the ∆ is equilateral.

Question 22

System of Equations

Answer 22

2 or more equations

Question 23

Substitution

Answer 23

1) Solve for x or y in one equation. Choose a variable with coefficient of 1.
2) Substitute it into the other equation.
3) Solve.

Question 24

Elimination

Answer 24

1) Eliminate x or y by adding the equations together.

2) Solve.

Question 25

hypotenuse

Answer 25

side opposite the right angle

• longest side of the ∆

Question 26

leg

Answer 26

the other 2 sides of right ∆

Question 27

Theorem 4-6 – Hypotenuse-Leg (HL) Theorem

Answer 27

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