Polygon Properties - Ch 5

Quadrilateral Sum Conjecture

The sum of the measures of the four angles of any quadrilateral is….

...360 degrees.

C-30 p. 256

D

C

B

A

m∠ + A m∠ + B m∠ + C m∠ = 360D °

Polygon Properties - Ch 5

Pentagon Sum Conjecture

The sum of the measures of the five angles of any pentagon is…

...540 degrees.

C-31 p. 256

E

DC

B

A

m∠ + A m∠ + B m∠ + C m∠ + D m∠ = 540E °

Polygon Properties - Ch 5

Polygon Sum Conjecture

The sum of the measures of the n interior angles of an n-gon is….

... 180o(n - 2).

C-32 p. 257

Polygon Properties - Ch 5

Exterior Angle Sum Conjecture

For any polygon, the sum of the measures of a set of exterior angles is….

...360 degrees.

C-33 p. 261

E

DC

B

A

m∠ + A m∠ + B m∠ + C m∠ + D m∠ = 360E °

Polygon Properties - Ch 5Equiangular Polygon Conjecture

You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas:….

180 - 360/n

C-34 p. 214

180(n - 2) / n

180(n−2)n

Polygon Properties - Ch 5

Kite Angles Conjecture

The _____________ angles of a kite

are _______________.

nonvertex

C-35 p. 267

congruent

Polygon Properties - Ch 5

Kite Diagonals Conjecture

The diagonals of a kite are….

...perpendicular.

C-36 p. 267

Polygon Properties - Ch 5Kite Diagonal Bisector Conjecture

The diagonal connecting the vertex angles of a kite is the ...

__________________________

... of the other diagonal.

C-37 p. 267

…perpendicular bisector...

Polygon Properties - Ch 5 Kite Angle Bisector Conjecture

The ______________ angles of a kite

are ______________ by a

___________ .

C-38 p. 267

vertex

bisected

diagonal

Polygon Properties - Ch 5Trapezoid Consecutive Angles Conjecture

The consecutive angles between the bases of a trapezoid are….

C-39 p. 268

…supplementary.

D

CB

A

m∠A+m∠B=180o

m∠C +m∠D=180o

Polygon Properties - Ch 5Isosceles Trapezoid Conjecture

The base angles of an isosceles trapezoid are ….

C-40 p. 269

…congruent.

∠A ≅∠B∠C ≅∠D

CD

BA

Polygon Properties - Ch 5Isosceles Trapezoid Diagonals Conjecture

The diagonals of an isosceles trapezoid are ….

C-41 p. 269

…congruent

CD

BA

AC ≅BD

Polygon Properties - Ch 5Three Midsegments Conjecture

The three midsegments of a triangle divide it into…

C-42 p. 273

...four congruent triangles.

Polygon Properties - Ch 5Triangle Midsegment Conjecture

A midsegment of a triangle is __________

to the third side and is ___________

the length of __________________.

C-43 p. 274

parallel

half

the third sideE

F

D

C

BA

Polygon Properties - Ch 5Trapezoid Midsegment Conjecture

The midsegment of a trapezoid is

_________ to the bases

and is equal in length to

__________________________________

C-44 p. 275

parallel

the average of the lengths of the bases.

Polygon Properties - Ch 5Parallelogram Opposite Angles Conjecture

The opposite angles of a parallelogram are…

C-45 p. 279

...congruent.D C

BA∠A ≅∠B∠C ≅∠D

Polygon Properties - Ch 5Parallelogram Consecutive Angles Conjecture

The consecutive angles of a parallelogram are…

C-46 p. 280

...supplementary.D C

BA

m∠ + A m∠ = 180B °m∠C + m∠D = 180°

Polygon Properties - Ch 5Parallelogram Opposite Sides Conjecture

The opposite sides of a parallelogram are…

C-47 p. 280

...congruent.D C

BA

AB ≅ CD and AD ≅ BC

Polygon Properties - Ch 5Parallelogram Diagonals Conjecture

The diagonals of a parallelogram…

C-48 p. 280

...bisect each other.

Polygon Properties - Ch 5

Double-edged Straightedge Conjecture

If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a …

C-49 p. 287

...rhombus.

Polygon Properties - Ch 5Rhombus Diagonals Conjecture

The diagonals of a rhombus are…

C-50 p. 288

...perpendicular..

.....and they...

...bisect each other.

Polygon Properties - Ch 5Rhombus Angles Conjecture

The ______________ of a rhombus

_______ the angles of the rhombus.

C-51 p. 288

diagonals

bisect

Polygon Properties - Ch 5

Rectangle Diagonals Conjecture

The diagonals of a rectangle are ___________

and they __________ each other.

C-52 p. 289

congruent

bisect

Polygon Properties - Ch 5Square Diagonals Conjecture

The diagonals of a square are

__________ and ______________

and they _________________.

C-53 p. 290

congruent

perpendicular

bisect each other