Angle Relationships
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Angle Relationships. Perpendicular Lines. Special intersecting lines that form right angles. Adjacent Angles. Angles in the same plane that have a common vertex and common side, but no common interior points. Vertical Angles. Two non-adjacent angles formed by two intersecting lines.

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Presentation Transcript
Angle relationships

Angle Relationships

Perpendicular Lines

Special intersecting lines that form right angles

Adjacent Angles

Angles in the same plane that have a common vertex and common side, but no common interior points

Vertical Angles

Two non-adjacent angles formed by two intersecting lines



Angle relationships

Angle Relationships

Perpendicular Lines

Special intersecting lines that form right angles

Adjacent Angles

Angles in the same plane that have a common vertex and common side, but no common interior points



Angle relationships

Angle Relationships

Perpendicular Lines

Special intersecting lines that form right angles

Adjacent Angles

Angles in the same plane that have a common vertex and common side, but no common interior points

Vertical Angles

Two non-adjacent angles formed by two intersecting lines


Angle relationships

1

3

4

2

Vertical Angles


Angle relationships

Angle Relationships

Linear Pair

Adjacent angles whose non-common sides are opposite rays



Angle relationships

Angle Relationships

Linear Pair

Adjacent angles whose non-common sides are opposite rays

Supplementary Angles

Two angles whose measures have a sum of 180 degrees


Angle relationships

1

2

Supplementary Angles


Angle relationships

Angle Relationships

Linear Pair

Adjacent angles whose non-common sides are opposite rays

Supplementary Angles

Two angles whose measures have a sum of 180 degrees

Complementary Angles

Two angles whose measures have a sum of 90 degrees



Angle relationships

Angle Relationships

Notes

Vertical angles are congruent

The sum of the measures of the angles in a linear pair is 180

Means perpendicular

M

N

Means M is perpendicular to N


Angle relationships

Angle Relationships

Notes

If a line is perpendicular to a plane, then that line is perpendicular to every line in the plane that it intersects


Angle relationships

N

M

O

Q

P

L

From this picture, you CAN assume

L, P, and Q are collinear

All points shown are coplanar

Rays PM, PN, PO, and LQ intersect at P

P is between L and Q

N is in the interior of angle MPO

Angle LPQ is a straight angle


Angle relationships

N

M

O

Q

P

L

From this picture, you CANNOT assume

Angle QPO is congruent to angle LPM

Angle OPN is congruent to angle LPM

Ray PN is perpendicular to ray PM

Ray LP is congruent to ray PQ

Ray PQ is congruent to ray PO

Angle QPO is congruent to angle OPN


Angle relationships

Angle Relationships

Checking for Understanding

J

G

I

H

K

From the picture, find the value of x

Angle GIJ = 9x –4 and angle JIH = 4x -11


Angle relationships

Angle Relationships

Checking for Understanding

3

2

4

1

5

Angle 1 and angle 4

Angle 1 and angle 2

Angle 3 and angle 4

Angle 1 and angle 5