- By
**nara** - Follow User

- 73 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Splash Screen' - nara

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Five-Minute Check (over Lesson 2–7)

CCSS

Then/Now

Postulate 2.10: Protractor Postulate

Postulate 2.11: Angle Addition Postulate

Example 1: Use the Angle Addition Postulate

Theorems 2.3 and 2.4

Example 2: Real-World Example: Use Supplement or Complement

Theorem 2.5: Properties of Angle Congruence

Proof: Symmetric Property of Congruence

Theorems 2.6 and 2.7

Proof: One Case of the Congruent Supplements Theorem

Example 3: Proofs Using Congruent Comp. or Suppl. Theorems

Theorem 2.8: Vertical Angles Theorem

Example 4: Use Vertical Angles

Theorems 2.9–2.13: Right Angle Theorems

Lesson MenuJustify the statement with a property of equality or a property of congruence.

A. Transitive Property

B. Symmetric Property

C. Reflexive Property

D. Segment Addition Postulate

5-Minute Check 1Justify the statement with a property of equality or a property of congruence.

A. Transitive Property

B. Symmetric Property

C. Reflexive Property

D. Segment Addition Postulate

5-Minute Check 2Justify the statement with a property of equality or a property of congruence.If H is between G and I, then GH + HI = GI.

A. Transitive Property

B. Symmetric Property

C. Reflexive Property

D. Segment Addition Postulate

5-Minute Check 3State a conclusion that can be drawn from the statement given using the property indicated.W is between X and Z; Segment Addition Postulate.

A.WX > WZ

B.XW + WZ = XZ

C.XW + XZ = WZ

D.WZ – XZ = XW

5-Minute Check 4State a conclusion that can be drawn from the statements given using the property indicated.

___

___

LMNO

A.

B.

C.

D.

5-Minute Check 5___ given using the property indicated.

Given B is the midpoint of AC, which of the following is true?

A.AB + BC = AC

B.AB + AC = BC

C.AB = 2AC

D.BC = 2AB

5-Minute Check 6Content Standards given using the property indicated.

G.CO.9 Prove theorems about lines and angles.

Mathematical Practices

3 Construct viable arguments and critique the reasoning of others.

6 Attend to precision.

CCSSYou identified and used special pairs of angles. given using the property indicated.

- Write proofs involving supplementary and complementary angles.

- Write proofs involving congruent and right angles.

Concept given using the property indicated.

Concept given using the property indicated.

Use the Angle Addition Postulate given using the property indicated.

CONSTRUCTIONUsing a protractor, a construction worker measures that the angle a beam makes with a ceiling is 42°. What is the measure of the angle the beam makes with the wall?

The ceiling and the wall make a 90 angle. Let 1 be the angle between the beam and the ceiling. Let 2 be the angle between the beam and the wall.

m1 + m2 = 90 Angle Addition Postulate

42 + m2 = 90 m1 = 42

42 – 42 + m2 = 90 – 42 Subtraction Property of Equality

m2 = 48 Substitution

Example 1Use the Angle Addition Postulate given using the property indicated.

Answer: The beam makes a 48° angle with the wall.

Example 1Find given using the property indicated.m1 if m2 = 58 and mJKL = 162.

A. 32

B. 94

C. 104

D. 116

Example 1Concept given using the property indicated.

Use Supplement or Complement given using the property indicated.

TIMEAt 4 o’clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands?

UnderstandMake a sketch of the situation. The time is 4 o’clock and the second hand bisects the angle between the hour and minute hands.

Example 260 + 60 = 120 given using the property indicated.

Use Supplement or Complement

PlanUse the Angle Addition Postulate and the definition of angle bisector.

Solve Since the angles are congruent by the definition of angle bisector, each angle is 60°.

Answer: Both angles are 60°.

CheckUse the Angle Addition Postulate to check your answer.

m1 + m2 = 120

120 = 120

Example 2QUILTING given using the property indicated.The diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD.

A. 20

B. 30

C. 40

D. 50

Example 2Concept given using the property indicated.

Concept given using the property indicated.

Concept given using the property indicated.

Concept given using the property indicated.

Given: given using the property indicated.

Prove:

Proofs Using Congruent Comp. or Suppl. Theorems

Example 3Proof: given using the property indicated.

Statements Reasons

1. m3 + m1 = 180;1 and 4 form a linear pair.

1. Given

2. 1 and 4 are supplementary.

2. Linear pairs are supplementary.

3. 3 and 1 are supplementary.

3. Definition of supplementary angles

4. 3 4

4. s suppl. to same are .

Proofs Using Congruent Comp. or Suppl. Theorems

Example 3In the figure, given using the property indicated.NYR andRYA form a linear pair,AXY and AXZ form a linear pair, and RYA andAXZ are congruent. Prove that NYR and AXY are congruent.

Example 3Statements Reasons given using the property indicated.

1. NYR and RYA, AXY and AXZ form linear pairs.

1. Given

2. NYR and RYA are supplementary. AXY and AXZ are supplementary.

2. If two s form a linear pair, then theyaresuppl.s.

3. Given

3. RYA AXZ

?

4. ____________

4.NYR AXY

Which choice correctly completes the proof?

Proof:

Example 3A. given using the property indicated. Substitution

B. Definition of linear pair

C. s supp. to the same or to s are .

D. Definition of supplementary s

Example 3Concept given using the property indicated.

Proof: given using the property indicated.

Statements Reasons

Use Vertical Angles

If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step.

1. 1 and 2are vertical s.

1. Given

2. 1 2

2. Vertical Angles Theorem

3. Definition ofcongruent angles

3. m1 = m2

4. d – 32 = 175 – 2d

4. Substitution

Example 4Use Vertical Angles given using the property indicated.

Statements Reasons

5. 3d – 32 = 175

5. Addition Property

6. 3d = 207

6. Addition Property

7. Division Property

7. d = 69

m1 = d – 32 m2 = 175 – 2d

= 69 – 32 or 37 = 175 – 2(69) or 37

Answer:m1 = 37 and m2 = 37

Example 4Concept given using the property indicated.

End of the Lesson given using the property indicated.

Download Presentation

Connecting to Server..