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# Distance & Midpoints Angle Measure - PowerPoint PPT Presentation

Distance & Midpoints Angle Measure. Notes 2 – Sections 1.3 & 1.4. Essential Learnings. Students will understand and be able to find distance and the midpoint of a segment. Students will be able to construct, copy and bisect segments.

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Distance & Midpoints Angle Measure

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## Distance & MidpointsAngle Measure

Notes 2 – Sections 1.3 & 1.4

### Essential Learnings

• Students will understand and be able to find distance and the midpoint of a segment.

• Students will be able to construct, copy and bisect segments.

• Students will understand and be able to measure and classify angles.

• Students will be able to identify and use congruent and special pairs of angles.

• Students will be able to identify perpendicular lines.

### Vocabulary

• The distance between two points is the length of the segment with those points as the endpoints.

• Midpoint – the point halfway between the endpoints of a segment.

x1

M

x2

### Distance Formula

• If P has the coordinates (x1,y1) and Q has coordinates (x2,y2) then:

### Example 1

• Find the distance between the pair of points. M(4,0) and L(-2,-3).

### Midpoint Formula

• If has the endpoints P(x1,y1) and Q(x2,y2) in the coordinate plane, then the midpoint M of is:

### Example 2

• Find the coordinates of the midpoint of a segment with endpoints W(12,2) and X(7,9).

### Example 3

• Find the coordinates of the missing endpoint if B is the midpoint .

A(1,7) and B (-3,1)

### Example 4

• Suppose M is the midpoint of . Use the given information to find the missing measure or value.

FM = 5x+13, MG = 5-3x, FG = ?

### Constructions

• Need compass!

Construct segment

Copy segment

Bisect a segment

### Vocabulary

• Ray – begins at a point and extends indefinitely in one direction.

• Angle – formed by two rays that have a common end point.

Q

P

PQ

### Vocabulary

• Vertex – the common endpoint of an angle.

• Side – one of the rays that make up an angle.

• Opposite rays – rays that share a common endpoint and are collinear.

### Angles

• Naming angles – use three letters with the vertex as the middle letter or can name the angle using the vertex but only if there is only one angle located at that vertex.

J

2

L

K

### Example 5

• Name all angles that have B as the vertex.

E

D

B

F

A

C

G

### Example 6

• Write another name for each angle.

∠DCB

∠BAC

∠4

D

B

2

5

1

3

4

A

C

E

### Measures of Angles

• Angles are measured in degrees.

Use your protractor to measure angles.

### Classifying Angles

Acute angle Right angle Obtuse angle

m∠A< 90⁰ m∠A= 90⁰ 90⁰<m∠A <180⁰

A

A

A

### Copying an Angle

• Use your compass.

### Angle Bisector

• Angle bisector – a ray that divides an angle into two congruent angles.

C

∠ABC ≅ ∠CBD

70⁰

70⁰

A

D

B

### Constructing Angle Bisector

• Use your compass.

### Example 7

Ray QS bisects ∠PQT. m∠PQT=60⁰ andm∠PQS=4x+14, solve for x.

T

S

P

Q

R

### Example 8

Ray KM bisects ∠NKL. m∠MKL=3x+13 andm∠NKM=6x-2, m∠NKL=?

N

M

J

K

L

### Assignment

Page 32: 19-29 odd, 41-53 odd

Page 41-44: 20-25, 37-41 odd, 64, 65

Signed Slip

Cover Textbook