Wayground
Triangle Proofs - Printable Math Worksheets year 9 - Wayground

Triangle Proofs

Lindsay Foster

Created by Lindsay Foster

20 questions

9th Grade

Math

Updated Oct 2026

Triangle Proofs is a Grade 9 mathematics worksheet that develops students’ ability to complete and interpret triangle congruence proofs. Across 20 questions—19 multiple choice and 1 multiple select—students identify missing statements and reasons in two-column proofs, use properties such as reflexive, vertical, and alternate interior angles, match corresponding parts, and determine whether triangles are congruent by SAS, ASA, AAS, or SSS. They also distinguish valid congruence tests from SSA, which does not prove congruence. This free printable worksheet helps students connect diagram evidence to the formal language and logical sequence of a proof. It is useful for guided practice, independent review, or checking readiness to write complete congruence arguments. An answer key is included so teachers can quickly verify students’ choices and address errors in both proof statements and reasons.

Worksheet settings

Font size

S
M
L
XL
WaygroundWorksheets

Triangle Proofs

Total questions: 20

Name
Class
Date
1.
What is statement #1?
What is statement #1?
a)
BC≅DC
b)
AC≅EC
c)
BC≅DC, AC≅EC
d)
∆BCA≅∆DCE
2.
What is statement #2?
What is statement #2?
a)
∠ABC≅∠EDC
b)
∠BCA≅∠DCE
c)
BC≅CD
d)
∠E≅∠A
3.
What is reason #3?
What is reason #3?
a)
SAS
b)
ASA
c)
SSS
d)
AAS
4.
What is the "statement" for step 3 of the proof?

What is the "statement" for step 3 of the proof?

a)

HA=HA

b)

HA=AH

c)

MA=AM

d)

MA=MA

5.
What is always the 1st statement in reason column of a proof?
a)
Prove
b)
Given
c)
Reason
d)
Statement
6.
What is the "statement" for step 3 of the proof?
What is the "statement" for step 3 of the proof? 
a)
∡EDA≅∡DCB
b)
∡AED≅∡BEC
c)
DE=CE
d)
∡AED≅∡CED
7.
Determine if the triangles are congruent, if "yes" state the theorem.
Determine if the triangles are congruent, if "yes" state the theorem.
a)
yes, SAS
b)
not congruent
c)
yes, ASA
d)
yes, AAS
8.
Which is NOT a test to prove triangles congruent?
a)
SAA
b)
SSS
c)
SSA
d)
SAS
9.
Use the congruence statement to find the missing part of the statement
Use the congruence statement to find the missing part of the statement
a)
WV
b)
WU
c)
VU
d)
WB
10.
What is #4 Statement?

What is #4 Statement?

a)

∠MNL ≌ ∠ONP

b)

MN ≌ ON

c)

N ≌ N

d)

MO ≌ OM

11.
What is #3 Reason?

What is #3 Reason?

a)

Same Line

b)

Perpendicular Lines

c)

Segment Bisector

d)

Reflexive Property

12.
What is #3 Reason?

What is #3 Reason?

a)

Alternate Exterior Angles

b)

Alternate Interior Angles

c)

Vertical Angles

d)

Angle Bisector

13.
Which of the following is a correct statement and reason for the proof shown?

Which of the following is a correct statement and reason for the proof shown?

a)

∠GEQ≅∠NEW\angle GEQ\cong\angle NEW Vertical

b)

WN‾≅GQ‾\overline{WN}\cong\overline{GQ} ; Prove

c)

∠G≅∠N\angle G\cong\angle N ; Alternate Interior

d)

∠W≅∠Q\angle W\cong\angle Q ; Alternate Interior

14.
State if the two triangles are congruent. If they are, state how you know.
State if the two triangles are congruent.  If they are, state how you know.
a)
A
b)
B
c)
C
d)
D
15.
What is the "statement" for step 2 of the proof?
What is the "statement" for step 2 of the proof?
a)
AD=AD
b)
AD=DA
c)
HD=DN
d)
HA = AN
16.
What is the "statement" for step 3 of the proof?
What is the "statement" for step 3 of the proof?
a)
AD=DA
b)
AN = AH
c)
HD=ND
d)
HD=DN
17.
When using hypotenuse leg (HL) in a proof, you must first state ...
a)
CPCTC.
b)
there are right triangles.
c)
that vertical angles are congruent.
d)
the reflexive property.
18.
What is the justification (reason)?
What is the justification (reason)?
a)
reflexive property
b)
definition of segment bisect
c)
definition of a midpoint
d)
substitution property
19.
What triangle congruence criteria is shown in the given diagram?
What triangle congruence criteria is shown in the given diagram?
a)
ASA
b)
AAS
c)
SSA
d)
HL
20.
A triangle with two congruent sides and two congruent angles (base angles) is called ...
a)
scalene
b)
equilateral
c)
isosceles
d)
obtuse
WaygroundAnswer Key

Triangle Proofs

Total questions: 20

1.
c) BC≅DC, AC≅EC
2.
b) ∠BCA≅∠DCE
3.
a) SAS
4.
b)

HA=AH

, a)

HA=HA

5.
b) Given
6.
b) ∡AED≅∡BEC
7.
b) not congruent
8.
c) SSA
9.
b) WU
10.
b)

MN ≌ ON

11.
d)

Reflexive Property

12.
b)

Alternate Interior Angles

13.
a)

∠GEQ≅∠NEW\angle GEQ\cong\angle NEW Vertical

14.
b) B
15.
c) HD=DN
16.
a) AD=DA
17.
b) there are right triangles.
18.
c) definition of a midpoint
19.
d) HL
20.
c) isosceles

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Triangle Proofs worksheet cover?

This Grade 9 worksheet uses 19 multiple-choice questions and 1 multiple-select question to practice completing triangle congruence proofs. Students identify missing statements and reasons, use reflexive, vertical-angle, and alternate-interior-angle relationships, match corresponding parts, and decide whether SAS, ASA, AAS, or SSS proves congruence.

How can I use this worksheet to teach triangle congruence proofs?

Begin by modeling how to read a proof one step at a time: identify the given information, select the statement supported by the diagram, and then choose its reason. Use the worksheet’s items on reflexive, vertical, and alternate interior angles to discuss how angle and segment relationships supply proof steps before asking students to classify a pair of triangles by SAS, ASA, AAS, or SSS.

What mistakes should I watch for when students complete this Triangle Proofs worksheet?

Students may confuse a missing statement with its reason, overlook that the first reason is typically “Given,” or reverse corresponding vertices when using a congruence statement. Watch especially for students who select SSA as a valid congruence test, miss reflexive relationships such as a segment being congruent to itself, or choose an angle relationship that does not match the diagram.

How do I assign and grade the Triangle Proofs worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for all 20 questions. Teachers can grade printable submissions by scanning student work with the Wayground for Teachers app, while the digital quiz supports online completion and grading.

How can I differentiate this triangle proof worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size for the proof-completion and multiple-choice items, or enable a dyslexia-friendly font. You can also translate the worksheet into another language; mathematical symbols and triangle-congruence notation remain central to the proof tasks.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion