Warm UP Are statements 1-3 ALWAYS, SOMETIMES, or NEVER true?

1. If two planes intersect, they intersect in a straight line.

2. If two lines intersect, they intersect at two different points

3. AB is another name for BA

Solve: HJ is twice JK . J is between H and K. If HJ = 4x and HK

= 78 find JK.

Find the error:

M is the midpoint of AB. Therefore AM ≅ MB.

A

N A

26

The congruent symbol should be an equal sign

WHAT IS AN ANGLE?

Angles

• An angle is a figure formed by two rays with the same

endpoint.

• The common endpoint is called the vertex of the angle.

The rays are the sides of the angle.

vertex

pg. 790

Naming Angles

A

I

H

G

B

C

F

D

E

Naming Angles

A

I

H

G

B

C

F

D

E

Naming Angles

A

I

H

G

B

C

F

D

E

Give Four Ways to Name this Angle

K

L

J

1

Write the different ways you can name the angles in the diagram.

RTQ, STR, 1, 2

Measuring Angles

• The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is 1/360 of a circle.

• We can use protractors to measure angles.

A Distinction!

ABC refers to the angle

mABC refers to the measurement of the angle

Let’s play with protractors!

Construct a 50 degree angle.

Construct a 35 degree angle that

faces up like a v.

Construct a 120 degree angle.

Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent.

Angle Bisector

An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM.

QS bisects PQR, mPQS = (5y – 1)°, and mPQR = (8y + 12)°. Find mPQS.

34°

Angle Addition Postulate

• If S is in the interior of PQR , then

mPQR = mPQS + mSQR .

mXWZ = 121° and mXWY = 59°. Find mYWZ.

mYWZ = mXWZ – mXWY

mYWZ = 121 – 59

mYWZ = 62

Add. Post.

Substitute the given values.

Subtract.

Pg. 25 (29-32)

•29. 16 ⅓

•30. 10

•31. 9

•32. 72°

The coordinate plane is formed by the intersection of two perpendicular number lines called axes. The point of intersection, called the origin, is at 0 on each number line. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis.

Points on the coordinate plane are described using ordered pairs. An ordered pair consists of an x-coordinate and a y-coordinate and is written (x, y). Points are often named by a capital letter.

The x-coordinate tells how many units to move left or right from the origin. The y-coordinate tells how many units to move up or down.

Reading Math

Graph each point.

A. T(–4, 4)

Start at the origin.

Move 4 units left and 4 units up.

B. U(0, –5)

Start at the origin. Move 5 units down.

• T(–4, 4)

• U(0, –5)

C. V (–2, –3)

Start at the origin.

Move 2 units left and 3 units down.

• V(–2, −3)

Locating Points in the Coordinate Plane

Name the quadrant in which each point lies.

A. E

Quadrant ll

B. F

no quadrant (y-axis)

C. G

Quadrant l

D. H Quadrant lll

•E

•F

•H

•G

x

y

Safari Montage Video

Pythagorean Theorem Video

Example Use the Distance Formula. Substitute the values for the coordinates of D and E into the Distance Formula.

Use the Pythagorean Theorem. Count the units for sides a and b.

a = 5 and b = 9.

c2 = a2 + b2

= 52 + 92

= 25 + 81

= 106

c = 10.3

The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3.

Check It Out!

Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

Midpoint Video