Proof Geometry
WKSHT 4.1
Chapter 4 Section 1 Worksheet
Name ________________________________hour____
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 __________
LN = __________
FH = __________
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
WKSHT 4.2
Chapter 4 Section 2 Worksheet
Name ________________________________hour____
Date:____/____/____ Score : ______% Recorded?___
Fill out the chart by drawing a picture in the first box, then writing a formula in the second box.
Angle Sum
Theorem
Third Angle
Theorem
Exterior Angle
Theorem
Find the missing angle measures.
1.
2.
3.
4.
5.
6.
7.
8.
9.
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
WKSHT 4.3
Chapter 4 Section 3 Worksheet
Name ________________________________hour____
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
WKSHT 4-5A
Chapter 4 Section 4-5 Worksheet
Name ________________________________hour____
Date:____/____/____ Score : ______% Recorded?___
In each circle, draw a picture to illustrate the triangle congruence shortcut.
SAS
HL
Triangle Congruence
Shortcuts
SSS
HA
ASA
AAS
LL
LA
Complete each statement with the information given. Give a reason for the triangle congruence.
1.
2.
3.
By:_________
By:_________
By:________
4.
5.
6.
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.
Y
P
Q
1
2
Diagram #1
To Prove: PYZ  QYZ
7. Given: ZPY  ZQY ; PYZ  QYZ ________
8. Given: 1 & 2 are right angles, PY  QY ________
Z
9. Given: PZ  QZ ; PY  QY _______
Diagram #2:
10. Given: A  C
Diagram #3:
11. To Prove: KXS  KDB ____________
To Prove: ABD  CBD
X
S
___________
B
K
D
B
A
D
C
Proof Geometry
WKSHT 4-5B
Chapter 4 Section 4-5 Worksheet
Name ________________________________hour____
Date:____/____/____ Score : ______% Recorded?___
For each of the following, complete a two-column or flow proof.
1. Given:
AB  CB,
AD  CD
B
A
C
Prove: mA  mC
D
2. Given: B & D are Right angles
1  2
AC  EC
A
Prove: C is the midpoint of BD
B
E
1
2
C
D
3. Given: PR  TR
P  T
Prove: Q  S
Q
P
1
R
2
T
S
J
4. Given: L is the midpoint of JM
J & M are right angles
K
2
L
1
N
Prove: KJ  NM
M
5. Given: SM  PQ
S  Q
M
S
N
SQ  PM
Prove: PN  SN
P
Q
Proof Geometry
WKSHT 4-5C
Chapter 4 Section 4-5 Worksheet
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
Name ________________________________hour____
Date:____/____/____ Score : ______% Recorded?___
4. Given: S  U ; TR bisects STU
Prove: SRT  URT
5. Given: S is the midpoint of QT , QR TU
Prove: QSR  TSU
6. Given: D  F
GE bisects DEF
Prove: DG  FG
Proof Geometry
WKSHT 4-5D
Chapter 4 Section 4-5 Worksheet
Complete a two-column or flow proof for each.
Name ________________________________hour____
Date:____/____/____ Score : ______% Recorded?___
1. Given: KM JL; KM  JL
Prove: K  L
D
2. Given: CDE is isosceles, with legs CD,&, ED
G is the midpoint of CE
G
C
E
Prove: C  E
3. Given: L is the midpoint of WE
WR ED
R
E
L
Prove: WRL  EDL
W
D
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
WKSHT 4-5E
Chapter 4 Section 4-5 Worksheet
Name ________________________________hour____
Date:____/____/____ Score : ______% Recorded?___
Complete a two-column or a flow proof for each.
M
1. Given: ML  MK , JK  KM
J  L
L
Prove: JM  KL
J
K
M
2. Given: JK  KM , JM  KL,
ML JK
Prove: ML  JK
J
K
L
3. Given: Q,&, S are right angles
1  2
Q
R
1
3
Prove: QP  SR
4
2
P
4. Given: Q,&, S are right angles
Q
1 3
QP  SR
Prove: 3  4
4
P
S
2
R
S
Proof Geometry
WKSHT 4.6
Chapter 4 Section 6 Worksheet
Name ________________________________hour____
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.
x = ________
11.
12.
x = __________
x = __________
Refer to the figure to answer the following questions.
13.
_________________
14.
_______________________
15.
________________
16.
________________
For problems 17-20, ABF is isosceles, CDF 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
WKSHT 4.7
Chapter 4 Section 7 Worksheet
Name ________________________________hour____
Date:____/____/____ Score : ______% Recorded?___
Position and label each triangle on the coordinate plane.
1. right ∆FGH with legs
2. isosceles ∆KLP with
a units and b units
base 𝐾𝑃 6b units long
3. isosceles ∆AND with
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 𝐴𝐶
Prove: 𝐵𝑀𝐴𝐶