Chapter 4 Review

Question 1

acute triangle

Answer 1

has 3 acute (less than 90°) angles

Question 2

equiangular triangle

Answer 2

has 3 congruent angles

Question 3

obtuse triangle

Answer 3

has 1 obtuse (more than 90°) angle

Question 4

right triangle

Answer 4

has 1 right (exactly 90°) angle

Question 5

equilateral triangle

Answer 5

has 3 congruent sides

Question 6

isosceles triangle

Answer 6

has at least 2 congruent sides

Question 7

scalene triangle

Answer 7

has no congruent sides

Question 8

Theorem 4.1: Triangle Angle-Sum Theorem

Answer 8

The sum of the measures of the angles of a triangle is 180.

Question 9

exterior angle of a triangle

Answer 9

formed by one side of the triangle and the extension of an adjacent side

Question 10

remote interior angles

Answer 10

the angles of a triangle that are not adjacent to a given exterior angle

Question 11

Theorem 4.2: Exterior Angle Theorem

Answer 11

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

EX. m∠4 = m∠1 + m∠2

Question 12

corollary

Answer 12

a theorem with a proof that follows as a direct result of another theorem

Question 13

Corollary 4.1: Right Angle Corollary

Answer 13

The acute angles of a right triangle are complementary.

Question 14

Corollary 4.2: Obtuse Angle Corollary

Answer 14

There can be at most one right or obtuse angle in a triangle.

EX. If m∠B ≥ 90°, then ∠A and ∠C are acute angles.

Question 15

congruent polygons

Answer 15

all of the parts of one polygon are congruent to the corresponding or matching parts of the other polygon

Question 16

Theorem 4.3: Third Angles Theorem

Answer 16

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

Question 17

Reflexive Property of Triangle Congruence

Answer 17

ΔABC ≅ ΔABC

Question 18

Symmetric Property of Triangle Congruence

Answer 18

If ΔABC ≅ ΔEFG, then ΔEFG ≅ ΔABC.

Question 19

Transitive Property of Triangle Congruence

Answer 19

If ΔABC ≅ ΔEFG and Δ EFG ≅ ΔJKL, then ΔABC ≅ ΔJKL.

Question 20

Postulate 4.1: Side-Side-Side (SSS) Congruence

Answer 20

If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.

EX. If Side AB ≅ XW,

Side AC ≅ XY, and

Side BC ≅ WY,

then ΔABC ≅ ΔXWY.

Question 21

included angle

Answer 21

the angle formed by two adjacent sides of a polygon

EX. ∠A is the included angle of sides b and c

Question 22

Postulate 4.2: Side-Angle-Side (SAS) Congruence

Answer 22

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 triangles are congruent.

EX. If Side AB ≅ DE,

Angle ∠B ≅ ∠E, and

Side BC ≅ EF,

then ΔABC ≅ ΔDEF.

Question 23

included side

Answer 23

the located between two consecutive angles of a polygon

EX. Side c is the included side

Question 24

Postulate 4.3: Angle-Side-Angle (ASA)

Answer 24

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.

If Angle ∠A ≅ ∠D,

and Side AC ≅ DF,

and Angle ∠C ≅ ∠F,

then ΔABC ≅ ΔDEF.

Question 25

Theorem 4.5: Angle-Angle-Side (AAS) Congruence

Answer 25

If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. EX. If Angle∠B ≅ ∠E, Angle ∠C ≅ ∠F , and Side AC ≅ DF, then ΔABC ≅ ΔDEF.

Question 26

legs, vertex, base, and base angles of an isosceles triangle

Answer 26

legs = the two congruent sides of the triangle vertex angle = the angle with the sides that are legs base = the side of the triangle opposite the vertex angle base angles = the two angles formed by the base and the congruent sides

Question 27

Theorem 4.10: Isosceles Triangle Theorem

Answer 27

If two sides of a triangle are congruent, then the angles opposite those sides are congruent. EX. If AB ≅ AC, then ∠C ≅ ∠B.

Question 28

Theorem 4.11: Converse of Isosceles Triangle Theorem

Answer 28

If two angles of a triangle are congruent, then the sides opposite those angles are congruent. EX. If ∠B ≅ ∠C, then AC ≅ AB.

Question 29

Corollary 4.3: Equilateral Triangle Corollary

Answer 29

A triangle is equilateral if and only if it is equiangular. EX. If ∠A ≅ ∠B ≅ ∠C, then AB ≅ BC ≅ CA.

Question 30

Corollary 4.4: Equilateral Triangle Corollary

Answer 30

Each angle of an equilateral triangle measure 60°. EX. If AB ≅ BC ≅ CA, then ∠A = ∠B = ∠C = 60°.