WARM UP

Solve for r 1. 124=πr²

2. 136=(4÷3)πr³

UNIT 1 REVIEW

SOLVING FOR VERTICAL ANGLES

Set angles ____________to each other and

solve60 X + 2

EQUAL

SOLVING FOR LINEAR PAIRS

Add together and set equal

to ______________

55

2X + 3

180

ADJACENT ANGLES

Angles that are next to each other but DON’T create a ____________line180

COMPLEMENTARY ANGLES =______

90

SUPPLEMENTARY ANGLES =______

180

THE PROPERTIES OF PARALLELOGRAMS

1. Opposite sides are congruent (AB=DC)

2. Opposite angles are congruent (D=B)

3. Consecutive angles are supplementary (A+D=180)

4. If one angle is right, then all angles are right.

5. The diagonals of a parallelogram bisect each other.

6. Each diagonal of a parallelogram separates it into two congruent triangles.

A B

CD

Example 1AWXYZ is a

parallelogram. Find YZ.

Def. of segs.

Substitute the given values.

Subtract 6a from both sides and add 4 to both sides.

Divide both sides by 2.

YZ = XW

8a – 4 = 6a + 10

2a = 14

a = 7

YZ = 8a – 4 = 8(7) – 4 = 52

opp. s

ALTERNATE INTERIOR

m

t

n

1 234

5 678

Interior angles that lie on different parallel lines and opposite sides of transversal. They are equal to each other!

ALTERNATE EXTERIOR Angles formed

outside the parallel lines and on opposite sides of transversal. They are equal!

m

t

n

1 234

5 678

CORRESPONDINGAngles that lie on the same

side of the transversal and are situated the same way on two parallel lines. Think:

Four CORNERS. They are equal!

m

t

n

1 234

5 678

VERTICALAcross the VERTEX from each other. They are equal!

m

t

n

1 234

5 678

CLASSIFYING TRIANGLES

Triangle – A figure formed when three noncollinear points are connected by segments.

E

DF

Angle

SideVertex

The sides are DE, EF, and DF.The vertices are D, E, and F.The angles are D, E, F.

BASE ANGLES THEOREM

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

If , thenACAB CB

CONVERSE OF BASE ANGLES THEOREM

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

If , thenCB ACAB

LEG

LEG

HYPOTENUSE

INTERIOR ANGLES

Exterior Angles

TRIANGLE SUM THEOREMThe measures of the three interior angles

in a triangle add up to be 180º.

x°

y° z°

x + y + z = 180°

The measure of the exterior angle is equal to the sum of two nonadjacent interior angles

1

2 3

m1+m2 =m3

Exterior Angle Theorem

The relationship shown in Example 1 is true for the three midsegments of every triangle.

Example 1

Find each measure.

BD = 8.5

∆ Midsegment Thm.

Substitute 17 for AE.

Simplify.

BD

6

18

4

X

Solving for

missing

sides

FIND X

100˚ 45˚x

X= 35

SOLVING FOR LINEAR PAIRS

Add together and set equal

to ______________

55

2X + 3

180