8.1 lesson

QuadrilateralsQuadrilaterals

You will learn to identify parts of quadrilaterals and find thesum of the measures of the interior angles of a quadrilateral.

1) Quadrilateral2) Consecutive3) Nonconsecutive4) Diagonal


A quadrilateral is a closed geometric figure with ____ sides and ____ vertices.four four

The segments of a quadrilateral intersect only at their endpoints.

Quadrilaterals Not Quadrilaterals

Special types of quadrilaterals include squares and rectangles.


A

B

CD

Quadrilaterals are named by listing their vertices in order.

There are several names for the quadrilateral below.

Some examples:

quadrilateral ABCD

quadrilateral BCDA

quadrilateral CDAB or

quadrilateral DABC

S R

Q

P


Any two sides, angles, or vertices of a quadrilateral are either __________ or _____________.

consecutive

nonconsecutive


S R

Q

P

Segments that join nonconsecutive vertices of a quadrilateral are called________.diagonals

S and Q arenonconsecutivevertices.

diagonal a is SQnonconsecutivevertices.


Q

T

S

R

Name all pairs of consecutive sides:

Name all pairs of nonconsecutive angles:

Name the diagonals:

RS and QR ST and RS

TQ and ST QR and TQ

S and Q R and T

and QS TR


D

C

B

AConsidering the quadrilateral to the right.

What shapes are formed if a diagonal is drawn? ___________two triangles

1

23

45

6

Use the Angle Sum Theorem (Section 5-2)to find m1 + m2 + m3 180

Use the Angle Sum Theorem (Section 5-2)to find m4 + m5 + m6 180

Find m1 + m2 + m3 + m4 + m5 + m6

180+ 180

360

This leads to the following theorem.


Theorem

8-1

The sum of the measures of the angles of a quadrilateral is

____.360

a°

d°

c°

b°

a + b + c + d = 360


A

D

C

BmA + mB + mC + mD = 360

x + 2x + x – 10 + 50 = 360

Find the measure of B in quadrilateral ABCD if A = x, B = 2x,C = x – 10, and D = 50.

4x + 40 = 360

4x = 320

x = 80

B = 2x

B = 2(80)

B = 160

8.1 lesson

Technology

Transcript of 8.1 lesson