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
