Proof Geometry Name ________________________________hour____WKSHT 4.1Chapter 4 Section 1 Worksheet Date:____/____/____ Score : ______% Recorded?___

Use a protractor to classify each triangle as acute, equiangular, obtuse, or right.

1. ________________________ 2. ________________________ 3. ________________________

4. ________________________ 5. ________________________ 6. ________________________

7. right 8. obtuse

________________________ ________________________

9. scalene 10. isosceles

________________________ ________________________

Find the value of x and the measure of each side of the triangle.11. ∆FGH is equilateral with FG = x + 5, 12. ∆LMN is isosceles, L is the vertex angle,GH = 3x -9, and FH = 2x – 2. LM = 3x – 2, LN = 2x + 1, and MN = 5x – 2

x = __________ FG = __________ x = __________ LM = __________

GH __________ FH = __________ LN = __________ MN = __________

Find the measures of the sides of ∆KPL and classify each triangle by its sides.

13. K(-3, 2), P(2, 1), L(-2, -3)

KP = __________ PL = __________ KL = __________ Classification:____________________

Proof Geometry Name ________________________________hour____WKSHT 4.2Chapter 4 Section 2 Worksheet Date:____/____/____ Score : ______% Recorded?___

Fill out the chart by drawing a picture in the first box, then writing a formula in the second box.

Find the missing angle measures.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Angle SumTheorem

Third AngleTheorem

Exterior AngleTheorem

Find the measure of each angle.

10.m∠1 = __________

11. m∠2 = ___________

12. m∠3 = ___________

Find the measure of each angle.

13. m∠1 = __________16. m∠ 4 = __________

14. m∠2 = __________17. m∠5 = __________

15. m∠3 = __________18. m∠ 6= __________

Find the value of x. No work – no credit.

19. 20.

21. 22.

Proof Geometry Name ________________________________hour____WKSHT 4.3Chapter 4 Section 3 Worksheet Date:____/____/____ Score : ______% Recorded?___

Identify the congruent triangles in each figure.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10.

Name the congruent angles and sides for each pair of congruent triangles.

11. 12. 13.

For questions 14-15, refer to the diagram.

14. Identify the triangles that appear to be congruent.

15. Name the congruent angles and sides for each pair of congruent triangles.

Proof Geometry Name ________________________________hour____WKSHT 4-5AChapter 4 Section 4-5 Worksheet Date:____/____/____ Score : ______% Recorded?___

In each circle, draw a picture to illustrate the triangle congruence shortcut.

Complete each statement with the information given. Give a reason for the triangle congruence.

1. 2. 3.

By:_________ By:_________ By:________

4. 5. 6.

HL

HA

LALLAASASA

SSS

SAS

Triangle CongruenceShortcuts

By:________ By:________ By:________

Write the triangle congruence abbreviation that would be used to show that the triangles are congruent. Treat each numbered exercise as a new problem.

Diagram #1 To Prove: Δ PYZ≃ΔQYZ

7. Given: ∠ ZPY ≃∠ZQY ;∠PYZ≃∠QYZ ________

8. Given: ∠1∧∠2 are right angles, PY ≃QY ________

9. Given: PZ≃QZ ; PY≃QY _______

Diagram #2: Diagram #3:10. Given: ∠ A≃∠C 11. To Prove: Δ KXS≃Δ KDB ____________

To Prove: Δ ABD≃ΔCBD

___________

D C

B

A

21

Z

QYP

DB

K

XS

Proof Geometry Name ________________________________hour____WKSHT 4-5BChapter 4 Section 4-5 Worksheet Date:____/____/____ Score : ______% Recorded?___

For each of the following, complete a two-column or flow proof.

1. Given:

AB≃CB ,AD≃CD

Prove: m∠ A=m∠C

2. Given: ∠B∧∠D are Right angles ∠1≃∠2

AC≃EC

Prove: C is the midpoint of BD21

E

DCB

A

D

C

B

A

3. Given: PR≃TR ∠P≃∠T

Prove: ∠Q≃∠ S

4. Given: L is the midpoint of JM ∠J∧∠M are right angles

Prove: KJ≃NM

5. Given: SM≃PQ ∠ S≃∠Q

SQ⊥PM

Prove: PN≃SN

21 N

M

L

J

K

QP

N

MS

2

1

TS

R

Q

P

Proof Geometry Name ________________________________hour____WKSHT 4-5CChapter 4 Section 4-5 Worksheet Date:____/____/____ Score : ______% Recorded?___Complete a two-column or flow proof for each.

1. Given: PQ‖SR and PQ≃SR

Prove: SP≃QR

2. Given: RS≃UT ; RT ≃US

Prove: ∠R≃∠U

3. Given: AB≃DB and C is the midpoint of AD

Prove: ∠ A≃∠D

4. Given: ∠ S≃∠U ;TR bisects ∠ STU

Prove: ∠ SRT≃∠URT

5. Given: S is the midpoint of QT , QR‖TU

Prove: ΔQSR≃ ΔTSU

6. Given: ∠D≃∠F

GE bisects ∠DEF

Prove: DG≃FG

Proof Geometry Name ________________________________hour____WKSHT 4-5DChapter 4 Section 4-5 Worksheet Date:____/____/____ Score : ______% Recorded?___Complete a two-column or flow proof for each.

1. Given: KM‖JL ;KM≃JL

Prove: ∠K≃∠L

2. Given: ΔCDE is isosceles, with legs CD ,&, ED G is the midpoint of CE

Prove: ∠C≃∠E

3. Given: L is the midpoint of WE

WR‖ED

Prove: ΔWRL≃Δ EDL

EGC

D

D

E

L

R

W

4. Given: DL bisects BN ∠XLN≃∠ XDB

Prove: LN≃DB

5. Given: Z is the midpoint of CT

CY‖TE

Prove: YZ≃EZ

6. Given: XZ bisects WY XZ ⊥WY

Prove: ∠W ≃∠Y

Proof Geometry Name ________________________________hour____WKSHT 4-5EChapter 4 Section 4-5 Worksheet Date:____/____/____ Score : ______% Recorded?___

Complete a two-column or a flow proof for each.

1. Given: ML⊥ MK , JK ⊥KM ∠J≃∠L

Prove: JM≃KL

2. Given: JK⊥ KM , JM≃KL ,

ML‖JK

Prove: ML≃JK

J K

LM

J K

LM

3. Given: ∠Q ,&,∠S are right angles ∠1≃∠2

Prove: QP≃SR

4. Given: ∠Q ,&,∠S are right angles

QP≃SR

Prove: ∠3≃∠4

4

3

2

1

P S

RQ

4

3

2

1

P S

RQ

Proof Geometry Name ________________________________hour____WKSHT 4.6Chapter 4 Section 6 Worksheet Date:____/____/____ Score : ______% Recorded?___

Find the value of x for each of the following.

1. 2. 3.

x = ________ x = __________ x = __________

4. 5. 6.

x = ________ x = __________ x = __________

7. 8. 9.

x = ________ x = __________ x = __________

10. 11. 12.

x = ________ x = __________ x = __________

Refer to the figure to answer the following questions.

13. _________________

14. _______________________

15. ________________

16. ________________

For problems 17-20, Δ ABF is isosceles, ΔCDF is equilateral, and m∠ AFD=150 . Find each measure.

17. m∠ AFB = ______ 18. m∠ A = ______

19. m∠CFD =______ 20. m∠ ABF = ______

Complete a proof for the following.

21.

Proof Geometry Name ________________________________hour____WKSHT 4.7Chapter 4 Section 7 Worksheet Date:____/____/____ Score : ______% Recorded?___

Position and label each triangle on the coordinate plane.1. right ∆FGH with legs 2. isosceles ∆KLP with 3. isosceles ∆AND witha units and b units base KP 6b units long base AD 5a long

Find the missing coordinates of each triangle.

4. 5. 6.

7. 8. 9.

10. Write a coordinate proof to prove that in an isosceles right triangle, the segment from the vertex of the right angle to the midpoint of the hypotenuse is perpendicular to the hypotenuse.

Given: isosceles right ∆ABC with ∆ABC the right angle and M the midpoint of ACProve: BMAC