I. Matching: Match the Following Vocabulary Words with Their Definitions/ Descriptions

Foundations of Math III

Unit 4: Logical Reasoning

in Geometry

1.1 Warm UpName:______

Date: ______

I. Matching: Match the following vocabulary words with their definitions/ descriptions.

____1. Linea. Two lines that intersect at right angles

____2. Segmentb. An infinite flat surface

____3. Perpendicular Linesc. Two coplanar lines that do not intersect

____4. Coplanard. Two non-coplanar lines that do not intersect

____5. Midpointe. Objects on the same plane

____6. Bisectf. An infinite collection of points in a straight path

____7.Non-collinearg. The point in the exact middle of a segment

____8. Planeh. Points not located on the same line

____9. Parallel Linesi. To cut in half

____10. Skew Linesj. Part of a line with endpoints

____11. Non-coplanar k. Points not located on the same plane

1.1Guided Practice Examples

Example 1

In the figure below, B is the midpoint of . Find x and AC.

A 2x + 12 B5x +10 C

Example 2

In the figure below, C is the midpoint of . Find x and AC.

5x – 6 2x

A C B

Example 3

In the figure below, Y is the midpoint of XZ. Find x.

X 4x - 6 Y Z

Example 4

In the figure below, G is the midpoint of . Find x and EG.

36 – y

1.1Homework

x = ______AC = ______2. y = ______EG = ______

3. a = ______HJ = ______4. y = ______KM = ______

5. x = ______NQ = ______ 6. b = ______QS = ______

1.2 Guided Practice Examples

Example 1

Find x, RS, and ST.R 2x–4 S 3x +7 T

Example 2

If XZ = 44, find y, XY and YZ.

Y Z

Example 3

If LN = 100, find a,

Example 4

If RT = 60, find x, RS, and ST.

3x – 12 2x – 8

R S T

1.2 Practice

x = ______, AB = ______, BC = ______5. x = ______MN = ______

MO = ______

x = ______, DE = ______, EF = ______

x = ______, GH = ______, HI = ______

6. x = ______, MN = ______

MO = ______

x = ______, JK = ______, KL = ______

1.2Homework Name ______

Given that point A lies between points C and T, find each missing value. (Hint: Draw and label a diagram for each problem.)

CA = 6

AT = ?

CT = 15

CA = 5.2

AT = 4.8

CT = ?

CA = ?

AT = 5

CT = 10

CA = 22

AT = ?

CT = 35

For each figure, find x and the indicated segment measure. Show all work on your own paper!

B is the midpoint of .

AB = 4x – 3

BC = x

AC = ?

E is the midpoint of .

DF = x + 6

DE = x – 1

EF = ?

bisects .

WB = x + 5

TW = 4x + 5

TB= ?

bisects at point O.

CO = 2x + 1

OT = x + 7

CT= ?

Use the Segment Addition Postulate to solve the following problems. Be sure to draw a diagram first!

If W is between R and S,, and ,

9. Solve for n.

10. Find RS.

11. Find WS.

1.3 Guided Practice Examples

Example 1 A

2x+12 mADC = 82

D B 82˚

Example 2

1.3 Practice Angle Addition Postulate – Coach/Student

1) 2)

3) 4)

1.3 HomeworkName______

Name the vertex of each angle.

1)7

2)6

3)8

4)4

Name the sides of each angle.

5)1

6)EFB

7)5

8)2

Write another name for each angle.

9)4

10) 7

11) EGC

12)AFE

13)Write and equation using the Angle Addition Postulate. Then solve for x and Find the measure of an AOB and BOC.

1.4 Warm Up Name ______

True or False? G

is congruent to .

intersects at point D.

C is between E and B.

is congruent to .

Points A, D, and C are collinear.

C is between A and F.

DC + CB =EB

∠ACG ≅ ∠GCB

ED + DC = EC

∠DCA ≅ ∠ACG

bisects segment AF

m∠ACG +m∠GCB = m∠ACB

m∠DCA +m∠GCB = m∠ACB

m∠DCA +m∠ACG = m∠ACB

True or False?

MP ⏊ NO ______

≅ OQ ______

andMRO are supplementary ______

MR + RP = MP ______

MR +RN = MN ______

mMNO + NRO = mMRO ______

m∠LRM +m ∠MRN = LRO ______

QRL ______

1.4 Guided Practice Examples

Example 1 A

OOB bisects AOC

2x + 12mAOC = 76

Example 2 L

bisectsLON

O 6y – 12mLON = 108

Example 3 O bisects AOC

mAOB = 48

A B

1.4 Homework

Use the figure below to decide whether each statement is true or false. Explain why each statement is true or false on your own paper!

bisects .
S is the midpoint of .
.
W bisects .
is longer than .
V is the midpoint of .
.
TB + BW = TW.

Mark the given information on the figure below. Then use the figure to help solve the following problems.

9) If mLQM = 7x – 12 and mNQM = 5x + 10, find x and mLQN.

10) If mOQP = 4x + 16 and mNQO = 6x + 4, find x and mOQP.

1.5 Guided Practice Examples

Example 1

⊥

2x -24

Example 2

Example 3

4x - 14

x = ______Find the measure of the adjacent angles. ______, ______

Example 4

x = ______

7x + 27

Example 5

R m∠ RST = 3x +24 x = ______

1.5 Homework

m∠ 1 = ______Name a right angle. ______

m∠ 2 = ______Name a pair of complementary angles. ______

m∠ 3 = ______Name a pair of vertical angles. ______

m∠ 4 = ______Name a linear pair of angles. ______

m∠ 5 = ______Name the vertex of <ABD. ______

m∠ 7 = ______Name the sides of <ABD. ______

m∠ 8 = ______Give another name for <5. ______

m∠ 9 = ______Give another name for <ABC. ______

Solve the following:

36° <1 and <2 are complimentary

12x 2 5x +14m<1 = 2x + 23 m<2 = 4x - 11

x = ______x = ______x = ______m<1 = ______m<2 =______

1.6 Practice Problems

Set 1:

1)Two angles are complementary. If one angle measures 4x + 3 and the other measures 2x + 21, find the measure of each angle.

2)is the perpendicular bisector of . If AB = 4x + 1 and AC = 3x + 42, find x, AB, and BC.

3)Find the measure of AEC and DEB.

4)is the perpendicular bisector of . If mDBE = 2x + 6 and mCBE = 2x, find mDBE and mCBE.

Set 2:

5)is the perpendicular bisector of . If mABE = 2x – 1 and mEBD=5x, find mABE and mEBD.

6)Find the measure of AEC and DEB.

7)is the perpendicular bisector of . If AB = 9x – 7 and AC = 2x + 21, find x, AB, and BC.

8)An angle measures 7x – 13. Its complement measures 4x + 15. Find the measure of each angle.

Homework 1.6 Name ______

Solve for the following using the definitions we have learned so far in this unit.

x = ______

y = ______

z = ______

3. 4.

x = ______X = ______

m<KML = ______

5. 6.

x= ______x = ______

X is the midpoint of WY = ______

7. 8.

m<AEC = 72°

______m<BDC = 89°

m<AED = 128°

m<BEC = ______

9. If ∠ A and ∠ B are complementary and m∠ A = 27˚, then m∠ B = ______

10. If R and S are complementary and mR = 46, then mS = ______

1.7Guided Practice

In the figure, XP and XT are opposite rays. XQ bisects PXS. For each situation, find the value of x and the measure of the indicated angle.

1)mSXT = 4x + 1, mQXS = 2x – 2, mQXT = 125; Find mQXS

2)mPXR = 3x, mRXT = 5x +20; Find mRXT

3)mRXQ = x + 15, mRXS = 5x – 7, mQXS = 3x +5; Find mRXS

4)mTXS = x + 3, mSXR = 2x + 9, mRXP = 42 – 7; Find mPXS

1.7 PracticeName______

Find the missing measures for the numbered angles.

m1 = 53

m2 = ______

m3 = ______

m4 = 28

m5 =

m6 = 44

m7 = ______

m8 = 37

m9 = ______

m10 = ______

m11 = ______

m12 = ______

m13 = ______

m14 = ______

m15 = ______

m16 = ______

m17 = ______

1.7HomeworkName______

Find the missing measures. Show all work on a separate piece of paper!

1) 2)

3)4)

5)6)

7)8)

9)Find the measures of two complementary angles A and B if mA = 7x + 4 and mB = 4x + 9.

10)The measure of an angle is five less than 4 times the measure of its supplement. Find the measures of both angles.

1.8 Warm Up With your partner and using your notecards, complete the following responses and permissions.

1.8 Practice Kuta Software – Angle Relationships

1.8 Homework

Matching: Using the picture to the right, state the type of angles named. Then state the line that is the transversal. If the angles do not have a transversal, state “none.” Finally, state whether the angles are supplementary or congruent.

corresponding B. alternate interior C. vertical D. linear pair E. Neither

TYPE TRANS.

∠1,∠ 5 ______
∠10, ∠6 ______
∠13, ∠ 15 ______
∠11, ∠ 5 ______
∠ 1, ∠ 3 ______
∠15, ∠4 ______
∠11, ∠7 ______
∠15, ∠12 ______
∠5, ∠8 ______

10. ∠1, ∠8 ______

11. ∠3, ∠6 ______

Using the picture to the right, find the following. Each problem is separate form the one before. (1 each)

m∠1 = 27˚, m∠4 = ______7. m∠8 = 23˚, m∠4 = ______
m∠6 = 104˚, m∠3 = ______8. m∠2 = 120˚, m∠5 = ______
m∠7 = 129˚, m∠8 = ______9. m∠3= 156˚, m∠8 = ______
m∠7 = 100˚, m∠2 = ______10. m∠1 = 29˚, m∠7 = ______
m∠ 4 = 53˚, m∠6 = ______

1.9Homework

Find the value for x in each of the following. Each of the lines are //.

1.2.

x = ______x= ______

3. 4.

x = ______x = ______

5.6.

x= ______x = ______

Foundations of Math III Due Date: ______

ConstructionsProject

For this project, you will use the six geometric constructions that you have learned in this unit to design and draw a picture of a single object. You are expected to use at least two of each of the constructions listed below in your picture. However, don’t use too many or your picture will be cramped with construction marks.

Construction A: Congruent Segments

Construction B: Congruent Angles

Construction C: Angle Bisector

Construction D: Perpendicular Line to a segment from a point on or off the segment

Construction E: Perpendicular Bisector of a segment

Construction F: Parallel Lines

You will turn in 5 items:

1)your version of the cat face that we constructed in class

2)colored copy of the cat face

3)the graded rough draft of your design

4)final version showing construction marks

5)a copy of the finished picture colored completely

Rough Draft:

You should make the rough draft of your picture on a piece of unlined paper. I would recommend playing with ideas several times before submitting a rough draft to me for comments. You will need a compass, a ruler, a pencil, and colored pencil. Place the letter of the construction used next to each set of construction marks (one letter for each construction, each time it is used). Use a colored pencil in your compass for the construction marks and use a regular pencil for all marks made without the compass.

Final Construction and Picture:

After I return your rough draft to you, be sure to read the comments and make corrections as you complete your final version. Next, make an identical copy of your picture by tracing it on a separate piece of paper but without any of your construction marks. Then color the picture using colored pencils.

RUBRIC

Item / Possible Points / Earned Points / Comments
Cat Face – Construction

drawing on unlined paper
complete
shows construction marks in a different color from picture marks
construction marks labeled with A-F
neat

/ 20
Cat Face – Colored Picture

traced accurately
colored attractively

/ 15
Rough Draft

drawing on unlined paper
picture is a recognizable object
shows construction marks in a different color from picture marks
construction marks labeled with A-F
neat
creative

/ 25
Final Version – Construction

drawing on unlined paper
shows construction marks in a different color from picture marks
construction marks labeled with A-F
incorporates feedback from rough draft
neat
creative

/ 25
Final Version – Colored Picture

traced accurately
colored attractively

/ 15
Total Points / 100

1.10Review for TestName______

Work through the following problems to review what you have learned in this unit.

Part I: Angles

Part II: Angle Bisector

Part III: Angle Terms

Part IV: Solving Problems involving angles.

1.10HomeworkName______

Work through the following problems to review what you have learned in this unit. You must complete the sections that you did not show mastery of on Day 10. The other sections are optional review.

Part I: Angles

Part II: Angle Bisector

Part III: Angle Terms

Part IV: Solving Problems involving angles.