7.1 Adjacent and Vertical Angles Part 1

7.1 Adjacent and Vertical Angles Part 1

Today's Goals:

​Classify angles.

Identify adjacent and vertical angles.

Angles are measured with DEGREES

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The measurement is usually written INSIDE the corner it applies to.​

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NOT USED FOR ANGLES:​

• inches​

• feet

• centimeters​

• millimeters

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Measuring Angles

Naming Angles

• Can be named using a number:

  • ∠1   means "ANGLE 1"

• Can be named using a single letter:

  • ∠A  means "ANGLE A" (not shown)

• Can be named using three letters (see next slide)

• ​m∠3  - means "MEASURE/SIZE OF "ANGLE 3"

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This symbol ∠  is NOT "less than"  that's this symbol:  <​

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Multiple Choice

If m∠A = m∠B  then what do you know?

• angle 'm' is less than angle 'A' and angle 'B'

• angle 'A' is less than angle 'B'

• angle 'A' and angle 'B' are the same size

• angle 'A' and angle 'B' are both greater than angle 'm'

​The MIDDLE LETTER is always a CORNER

Find the angle by following the letters:

angle ∠ABC  is the entire L shape

• ∠ABD  is the same as ∠DBA  

  • It's also the same as ∠1  

• ∠DBC  is the same as ∠CBD 

  • It's also the same as  ∠2​

3 LETTERS

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Multiple Choice

What is the THREE LETTER name for ∠3 ?

• ace

• eca

• ACE

• ECA

Multiple Choice

Which of these is NOT AN ACTUAL ANGLE in the image?

• ∠ACD

• ∠BCE

• ∠ECB

• ∠DBC

• ∠ECD

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• They're exactly 90^o

• ​They look like a perfect T or L

• See a square in the corner? (right angle!)

  • DO NOT ASSUME an angle is exactly 90^o

  • >> unless the picture or directions say so​

Right Angles

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Multiple Choice

Based on the image, what is m∠R  ?

• $$150\degree$$  

• $$90\degree$$  

• 180 $$\degree$$  

• It's impossible to tell.

Multiple Choice

Classify this angle.

• Straight angle

• Supplementary angles

• Acute angle

• Obtuse angle

Multiple Choice

This pizza is cut into ________ angles.

• right

• obtuse

• acute

• straight

Multiple Choice

What type of angle has a measurement of 180^o?

• acute

• obtuse

• right

• straight

Multiple Choice

Classify the angle

• acute
• obtuse
• right
• straight

Multiple Choice

The corners of this road sign are what type of angles?

• Obtuse

• Acute

• Straight

• Right

Multiple Choice

This angle is an example of what type of angle?

• right
• acute
• obtuse
• straight

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Adjacent means "NEXT TO"​

Adjacent angles SHARE A WALL

Adjacent angles also SHARE A CORNER/VERTEX

• ∠Q  and  ∠R  are adjacent

• ∠Q  and  ∠T  are adjacent

• ∠Q  and  ∠S  are not adjacent (they're "across the street" neighbors!)

Adjacent Angles

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Vertical Angles are opposite angles

Vertical Angles are formed by the intersection of two lines.

Vertical angles are congruent angles, meaning they have the same measure.

• ∠Q  and  ∠S  are vertical

• ∠T  and  ∠R  are vertical

Vertical Angles

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Multiple Choice

Which are pairs of vertical angles?

• ∠COB & ∠COA
• ∠AOD & ∠AOC
• ∠COB & ∠AOD
• ∠BOD & ∠AOD

Multiple Choice

Which are pairs of adjacent angles?

• ∠COB & ∠DOA
• ∠AOD & ∠AOC
• ∠COB & ∠AOD
• ∠BOD & ∠AOC

Multiple Choice

Name the vertical angle to
∠h.

• ∠f
• ∠i
• ∠g
• ∠j

Multiple Choice

What angle pair is pictured?

• Alternate Interior Angles
• Supplementary Angles
• Vertical Angles
• Corresponding Angles

Multiple Choice

Vertical angles are always

• acute
• total 180 degrees
• congruent (equal measures)
• adjacent angles

Multiple Choice

∠1 and ∠2 are _____________

• Complementary

• Supplementary

• Adjacent

• Vertical