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Distance & Midpoints Angle MeasurePowerPoint Presentation

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

Measures of Angles

- Angles are measured in degrees.
Use your protractor to measure angles.

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.

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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