Distance midpoints angle measure
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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

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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<m∠A <180⁰

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


Constructing angle bisector

Constructing Angle Bisector

  • Use your compass.


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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