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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

Distance & MidpointsAngle Measure

Notes 2 – Sections 1.3 & 1.4

essential learnings
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
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
Distance Formula
  • If P has the coordinates (x1,y1) and Q has coordinates (x2,y2) then:
example 1
Example 1
  • Find the distance between the pair of points. M(4,0) and L(-2,-3).
midpoint formula
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
Example 2
  • Find the coordinates of the midpoint of a segment with endpoints W(12,2) and X(7,9).
example 3
Example 3
  • Find the coordinates of the missing endpoint if B is the midpoint .

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

example 4
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
Constructions
  • Need compass!

Construct segment

Copy segment

Bisect a segment

vocabulary1
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

vocabulary2
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
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
Example 5
  • Name all angles that have B as the vertex.

E

D

B

F

A

C

G

example 6
Example 6
  • Write another name for each angle.

∠DCB

∠BAC

∠4

D

B

2

5

1

3

4

A

C

E

measures of angles
Measures of Angles
  • Angles are measured in degrees.

Use your protractor to measure angles.

classifying angles
Classifying Angles

Acute angle Right angle Obtuse angle

m∠A< 90⁰ m∠A= 90⁰ 90⁰

A

A

A

copying an angle
Copying an Angle
  • Use your compass.
angle bisector
Angle Bisector
  • Angle bisector – a ray that divides an angle into two congruent angles.

C

∠ABC ≅ ∠CBD

70⁰

70⁰

A

D

B

example 7
Example 7

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

T

S

P

Q

R

example 8
Example 8

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

N

M

J

K

L

assignment
Assignment

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

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

Signed Slip

Cover Textbook

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