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Triangle congruence proofs - Printable Math Worksheets class 12 - Wayground

Triangle congruence proofs

John Spyker

Created by John Spyker

16 questions

12th Grade

Math

Updated Apr 2026

Triangle Congruence Proofs is a Grade 12 mathematics worksheet that develops students’ ability to determine whether triangles are congruent and justify their conclusions. Across 16 diagram-based questions, students identify appropriate criteria such as ASA, AAS, SAS, SSS, and HL; recognize insufficient information; use reflexive, vertical-angle, midpoint, and alternate-interior-angle relationships; complete proof steps; label corresponding parts; and connect congruence with rigid motions and CPCTC. Two math-response items also require students to solve for x using given segment and angle expressions. The worksheet combines dropdowns, hotspot selection, image drag-and-drop, multiple-select items, a drag-and-drop response, and algebraic responses, making it useful for guided practice, independent review, or an assessment of proof readiness. It is a free printable worksheet with a complete answer key, and its varied formats give teachers multiple ways to check whether students can identify evidence and apply it correctly in triangle congruence proofs.

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Triangle congruence proofs

Total questions: 16

Name
Class
Date
1.
Given the information in the image, you can deduce that the triangles are ​ because ​ ​

Given the information in the image, you can deduce that the triangles are ​ (a)   because ​ (b)   ​

Choose from the below words
of the ASA Triangle congruence postulate.
of the SSA Triangle congruence theorem.
of the SSS Triangle congruence postulate.
of the HL Triangle congruence postulate.
of the AAS Triangle congruence theorem.
of the SAS Triangle congruence theorem.
there is not enough information given.
congruent
not congruent
2.
Given the information in the image, you can deduce that the triangles are ​ because ​ ​

Given the information in the image, you can deduce that the triangles are ​ (a)   because ​ (b)   ​

Choose from the below words
of the ASA Triangle congruence postulate.
of the SSA Triangle congruence theorem.
of the SSS Triangle congruence postulate.
of the HL Triangle congruence postulate.
of the AAS Triangle congruence theorem.
of the SAS Triangle congruence theorem.
there is not enough information given.
congruent
not congruent
3.
Given the information in the image, you can deduce that the triangles are ​ because ​ ​

Given the information in the image, you can deduce that the triangles are ​ (a)   because ​ (b)   ​

Choose from the below words
of the ASA Triangle congruence postulate.
of the SSA Triangle congruence theorem.
of the SSS Triangle congruence postulate.
of the HL Triangle congruence postulate.
of the AAS Triangle congruence theorem.
of the SAS Triangle congruence theorem.
there is not enough information given.
congruent
not congruent
4.
Given the information in the image, you can deduce that the triangles are ​ because ​ ​

Given the information in the image, you can deduce that the triangles are ​ (a)   because ​ (b)   ​

Choose from the below words
of the ASA Triangle congruence postulate.
of the SSA Triangle congruence theorem.
of the HL Triangle congruence postulate.
of the AAS Triangle congruence theorem.
of the SAS Triangle congruence theorem.
there is not enough information given.
congruent
not necessarily congruent
of the SSS Triangle congruence postulate.
5.

You are trying to prove △MXC≅△LXC. Identify the components of the triangles on the diagram that are congruent due to the reflexive property help prove their congruence by selecting the points which define the components.

A
B
C
D
6.

Fill in the proof with the labels below.

a)

AAS congruence theorem

b)

Definition of midpoint

c)

∠SEM

d)

CPCTC

e)

△SEM ≅ △KMR

f)

SAS congruence postulate

g)

SM

h)

∠SMR

i)

RM ≅ EM

j)

Alternate internal ∠’s are ≅

1
2
3
4
5
6
7
8
9
10
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
7.
Given the image, mark all true statements

Given the image, mark all true statements

a)

∠SEO ≅ ∠STZ

b)

EO ≅ TZ

c)

SO ≅ SZ

d)

∠ESO ≅ ∠TZS

e)

∠YTE ≅ ∠YES

8.
What additional information is needed to prove that △MYG ≅ △MYR?​ ​

What additional information is needed to prove that △MYG ≅ △MYR?​ ​ (a)  

Choose from the below words
EO ≅ TE
∠YTE ≅ ∠YES
∠ESO ≅ ∠TES
GM ≅ MK
GR ≅ GR
OT ≅ ZE
∠OMS ≅ ∠MSE
9.
Mark the angle pairs which are congruent due to the presence of transversal HK which would help prove that triangles RXH and…

Mark the angle pairs which are congruent due to the presence of transversal HK which would help prove that triangles RXH and KXN are congruent.

a)

∠RXK ≅ ∠HXN

b)

∠RHX ≅ ∠NKX

c)

∠CRN ≅ ∠TNC

d)

∠RHX ≅ ∠KXN

10.

Label the blank triangle with the corresponding triangle part.

a)

|||

b)

|

c)

||

d)

)))

e)

))

f)

)

1
2
3
4
5
6
1)
2)
3)
4)
5)
6)
11.

In terms of congruence, (a)   shows that ​ (b)   occurred by manipulating the figures in a manner which demonstrate that (c)   are (d)   .​

Choose from the below words
mapping
rigid motions
both the corresponding sides and angles
the same measure
dialtions
both dilations and rigid motions
the verticies
the corresponding sides
translating
identical
12.
Given: SP = 2x-3 SE = 10-2x KN = 2x+1 RE= 3x-2 RP = 3x-3 FN=2y+3 Solve for x

Given:

SP = 2x-3

SE = 10-2x

KN = 2x+1

RE= 3x-2

RP = 3x-3

FN=2y+3

Solve for x

13.
Given: m∠SPR = (25x +5) m ∠SER= (1+12x) m∠YKN= (11x+9) m∠FYK= (27x-1) Solve for x

Given:

m∠SPR= (25x +5)

m∠SER= (1+12x)

m∠YKN= (11x+9)

m∠FYK= (27x-1)

Solve for x

14.
You are trying to prove triangles A and B congruent. Given the information depicted on the diagram. What is the reason you…

You are trying to prove triangles A and B congruent. Given the information depicted on the diagram. What is the reason you would mark the blue, single arc angles congruent?

a)

The two angles are corresponding parts of the two triangles in question.

b)

Alternate internal angles of a transversal are congruent.

c)

The reflexive property of congruence.

d)

The transversal cuts through two parallel lines.

e)

These angles are Vertical angles and therefore are congruent

15.
You are trying to prove triangles A and B congruent. Given the information depicted on the diagram. What is the reason you…

You are trying to prove triangles A and B congruent. Given the information depicted on the diagram. What is the reason you would mark the blue, single arc angles congruent?

a)

The two angles are corresponding parts of the two triangles in question.

b)

Alternate internal angles of a transversal are congruent.

c)

The reflexive property of congruence.

d)

These angles are Vertical angles and therefore are congruent.

e)

It meets the criteria for the angle addition postulate.

16.
You are trying to prove triangles A and B congruent. In the Given Statement, you were told that Triangle C and D are…

You are trying to prove triangles A and B congruent. In the Given Statement, you were told that Triangle C and D are congruent. What is the reason you would mark the blue single and blue double marked line segments congruent?

a)

Corresponding Parts of Congruent Triangles are Congruent.

(CPCTC)

b)

Definition of Midpoint

c)

Congruent Transversal Line Segment Postulate

d)

Definition of Perpendicular Lines

e)

Segment Addition Postulate

WaygroundAnswer Key

Triangle congruence proofs

Total questions: 16

1.
congruent, of the ASA Triangle congruence postulate.
2.
congruent, of the AAS Triangle congruence theorem.
3.
congruent, of the SSS Triangle congruence postulate.
4.
not necessarily congruent, there is not enough information given.
5.
6.
f
g
h
b
c
e
i
a
d
j
7.
a)

∠SEO ≅ ∠STZ

, b)

EO ≅ TZ

, c)

SO ≅ SZ

8.
GM ≅ MK
9.
a)

∠RXK ≅ ∠HXN

, b)

∠RHX ≅ ∠NKX

10.
a
b
c
d
e
f
11.
mapping, rigid motions, both the corresponding sides and angles, the same measure
12.

33

13.

22

14.
a)

The two angles are corresponding parts of the two triangles in question.

, b)

Alternate internal angles of a transversal are congruent.

, d)

The transversal cuts through two parallel lines.

15.
a)

The two angles are corresponding parts of the two triangles in question.

, d)

These angles are Vertical angles and therefore are congruent.

16.
a)

Corresponding Parts of Congruent Triangles are Congruent.

(CPCTC)

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FAQs

What does the Triangle Congruence Proofs worksheet cover?

This Grade 12 worksheet asks students to decide whether pairs of triangles are congruent, select or complete the justification, and identify evidence such as ASA, AAS, SAS, SSS, or HL. Its 16 items use diagrams, dropdowns, multiple-select questions, hotspot and drag-and-drop proof tasks, labeling, and math responses to build skill in matching corresponding parts, using angle and segment relationships, and solving for unknown measures.

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

Begin by reviewing how side and angle markings, shared sides, vertical angles, alternate interior angles, and midpoint information supply proof statements. Then have students complete the diagram-based identification items before moving to the proof-labeling and corresponding-parts questions; ask them to name both the evidence and the congruence criterion rather than selecting a theorem without explanation. Finish with the algebraic items to connect congruent measures with solving for x.

What mistakes should I watch for when students complete this triangle congruence worksheet?

Watch for students choosing a criterion from the number of markings without checking whether the angles are included, confusing SSA with a sufficient congruence condition, or overlooking a shared segment through the reflexive property. In the multiple-select items, students may select statements that are merely plausible instead of verifying the marked correspondence, and in the proof and math-response items they may mislabel parts or solve the angle and segment equations incorrectly.

How do I assign and grade this triangle congruence worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the dropdown, selection, proof, labeling, and math-response items. Printable student submissions can be graded by scanning the completed work with the Wayground for Teachers app.

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

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the diagram-based prompts, proof labels, and algebraic expressions are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the same triangle-congruence question formats.

Where can I find more worksheets like this on Wayground?

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

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