What else is needed to prove triangle CAB is congruent to triangle CAD by ASA? — triangle a b c with segment b d to the base, labeled B, C, D, A

∠ CAB is congruent to ∠ CAD

Congruent triangles worksheet

Three matching parts prove two triangles congruent, but only in the right pattern: three sides, two sides with the angle between them, two angles with a side, or a hypotenuse and a leg of right triangles. Two sides and an angle not between them (SSA) proves nothing, and neither do three angles. In a congruence statement the letters line up: the first vertex matches the first.

Not quite the one you need? Same words, different skill:

Similar Triangles (Geometry). AA, SSS, SAS, and the missing side.

The questions

What to include

SSS, SAS, ASA, AAS, HL, or not enough

Corresponding parts from a congruence statement

Corresponding parts written in x

What else is needed?

Write the congruence statement

Triangles that share a side or meet at a crossing

Right triangles: HL, LL, HA, LA

What else is needed, from a marked drawing (shared sides, crossings, right triangles)

Matching parts when the triangles share a side

Question order

Printing options

Working space

Answer key

Print an answer key on a second page

Version

On the answer key. Type it in to get that sheet back.

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Sigma Prep · sigmaprep.io/worksheets Name Congruent Triangles Date Period Answer each question. Name the congruence postulate, if any Are the triangles congruent? If so, by which postulate? Name the postulate that shows the triangles are congruent, if there is one. Name the postulate that proves the triangles congruent, or say there is not enough information. Which postulate proves the triangles congruent, if any? Which postulate proves the triangles congruent, if any? Name the postulate that shows the triangles are congruent, if there is one. Name corresponding parts from a congruence statement $△ J K L ≅ △ M O N$ . What corresponds to $\overline{K L}$ ? $△ A B C ≅ △ E F D$ . What corresponds to $∠ A$ ? $△ R S T ≅ △ U V W$ . What corresponds to $\overline{T R}$ ? Use corresponding parts to find $x$ or a part $△ A B C ≅ △ Y X Z$ , $m ∠ A = {(4 x - 40)}^{\circ}$ and $m ∠ Y = {(7 x - 94)}^{\circ}$ . Find $m ∠ Y$ . $△ A B C ≅ △ D E F$ , $m ∠ B = {(x + 91)}^{\circ}$ and $m ∠ E = {(2 x + 82)}^{\circ}$ . Find $x$ . $△ J K L ≅ △ F D E$ , $J K = 3 x - 14$ and $F D = 6 x - 47$ . Find $x$ . Name what else is needed Given $\overline{A B} ≅ \overline{D E}$ and $\overline{C A} ≅ \overline{F D}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SSS? Given $∠ A ≅ ∠ D$ and $\overline{A B} ≅ \overline{D E}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS? Given $\overline{A B} ≅ \overline{D E}$ and $\overline{B C} ≅ \overline{E F}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS? Write the congruence statement The triangles are congruent. Complete the statement: $△ A C B ≅ △$ The triangles are congruent. Complete the statement: $△ Q P R ≅ △$ The triangles are congruent. Complete the statement: $△ H G I ≅ △$ Name the right-triangle congruence rule The marks show the triangles are congruent. By which rule: HL, LL, HA or LA? Which rule proves the right triangles congruent: HL, LL, HA or LA? Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Congruent Triangles

Date Period

Answer each question.

Name the congruence postulate, if any
Are the triangles congruent? If so, by which postulate?
Name the postulate that shows the triangles are congruent, if there is one.
Name the postulate that proves the triangles congruent, or say there is not enough information.
Which postulate proves the triangles congruent, if any?
Which postulate proves the triangles congruent, if any?
Name the postulate that shows the triangles are congruent, if there is one.

Name corresponding parts from a congruence statement
$△ J K L ≅ △ M O N$ . What corresponds to $\overline{K L}$ ?
$△ A B C ≅ △ E F D$ . What corresponds to $∠ A$ ?
$△ R S T ≅ △ U V W$ . What corresponds to $\overline{T R}$ ?

Use corresponding parts to find $x$ or a part
$△ A B C ≅ △ Y X Z$ , $m ∠ A = {(4 x - 40)}^{\circ}$ and $m ∠ Y = {(7 x - 94)}^{\circ}$ . Find $m ∠ Y$ .
$△ A B C ≅ △ D E F$ , $m ∠ B = {(x + 91)}^{\circ}$ and $m ∠ E = {(2 x + 82)}^{\circ}$ . Find $x$ .
$△ J K L ≅ △ F D E$ , $J K = 3 x - 14$ and $F D = 6 x - 47$ . Find $x$ .

Name what else is needed
Given $\overline{A B} ≅ \overline{D E}$ and $\overline{C A} ≅ \overline{F D}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SSS?
Given $∠ A ≅ ∠ D$ and $\overline{A B} ≅ \overline{D E}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS?
Given $\overline{A B} ≅ \overline{D E}$ and $\overline{B C} ≅ \overline{E F}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS?

Write the congruence statement
The triangles are congruent. Complete the statement:
$△ A C B ≅ △$
The triangles are congruent. Complete the statement:
$△ Q P R ≅ △$
The triangles are congruent. Complete the statement:
$△ H G I ≅ △$

Name the right-triangle congruence rule
The marks show the triangles are congruent. By which rule: HL, LL, HA or LA?
Which rule proves the right triangles congruent: HL, LL, HA or LA?



Sigma Prep · sigmaprep.io/worksheets Name Congruent TrianglesAnswer keyVersion 1 Date Period Answer each question. Name the congruence postulate, if any Are the triangles congruent? If so, by which postulate?ASA Name the postulate that shows the triangles are congruent, if there is one.HL Name the postulate that proves the triangles congruent, or say there is not enough information.AAS Which postulate proves the triangles congruent, if any?Not enough information Which postulate proves the triangles congruent, if any?SAS Name the postulate that shows the triangles are congruent, if there is one.SSS Name corresponding parts from a congruence statement $△ J K L ≅ △ M O N$ . What corresponds to $\overline{K L}$ ? $\overline{O N}$ $△ A B C ≅ △ E F D$ . What corresponds to $∠ A$ ? $∠ E$ $△ R S T ≅ △ U V W$ . What corresponds to $\overline{T R}$ ? $\overline{W U}$ Use corresponding parts to find $x$ or a part $△ A B C ≅ △ Y X Z$ , $m ∠ A = {(4 x - 40)}^{\circ}$ and $m ∠ Y = {(7 x - 94)}^{\circ}$ . Find $m ∠ Y$ . $32^{\circ}$ $△ A B C ≅ △ D E F$ , $m ∠ B = {(x + 91)}^{\circ}$ and $m ∠ E = {(2 x + 82)}^{\circ}$ . Find $x$ . $9$ $△ J K L ≅ △ F D E$ , $J K = 3 x - 14$ and $F D = 6 x - 47$ . Find $x$ . $11$ Name what else is needed Given $\overline{A B} ≅ \overline{D E}$ and $\overline{C A} ≅ \overline{F D}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SSS? $\overline{B C} ≅ \overline{E F}$ Given $∠ A ≅ ∠ D$ and $\overline{A B} ≅ \overline{D E}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS? $\overline{C A} ≅ \overline{F D}$ Given $\overline{A B} ≅ \overline{D E}$ and $\overline{B C} ≅ \overline{E F}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS? $∠ B ≅ ∠ E$ Write the congruence statement The triangles are congruent. Complete the statement: $△ A C B ≅ △$ $△ F D E$ The triangles are congruent. Complete the statement: $△ Q P R ≅ △$ $△ K L J$ The triangles are congruent. Complete the statement: $△ H G I ≅ △$ $△ O M N$ Name the right-triangle congruence rule The marks show the triangles are congruent. By which rule: HL, LL, HA or LA?HL Which rule proves the right triangles congruent: HL, LL, HA or LA?HA Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Congruent TrianglesAnswer keyVersion 1

Date Period

Answer each question.

Name the congruence postulate, if any
Are the triangles congruent? If so, by which postulate?ASA
Name the postulate that shows the triangles are congruent, if there is one.HL
Name the postulate that proves the triangles congruent, or say there is not enough information.AAS
Which postulate proves the triangles congruent, if any?Not enough information
Which postulate proves the triangles congruent, if any?SAS
Name the postulate that shows the triangles are congruent, if there is one.SSS

Name corresponding parts from a congruence statement
$△ J K L ≅ △ M O N$ . What corresponds to $\overline{K L}$ ? $\overline{O N}$
$△ A B C ≅ △ E F D$ . What corresponds to $∠ A$ ? $∠ E$
$△ R S T ≅ △ U V W$ . What corresponds to $\overline{T R}$ ? $\overline{W U}$

Use corresponding parts to find $x$ or a part
$△ A B C ≅ △ Y X Z$ , $m ∠ A = {(4 x - 40)}^{\circ}$ and $m ∠ Y = {(7 x - 94)}^{\circ}$ . Find $m ∠ Y$ . $32^{\circ}$
$△ A B C ≅ △ D E F$ , $m ∠ B = {(x + 91)}^{\circ}$ and $m ∠ E = {(2 x + 82)}^{\circ}$ . Find $x$ . $9$
$△ J K L ≅ △ F D E$ , $J K = 3 x - 14$ and $F D = 6 x - 47$ . Find $x$ . $11$

Name what else is needed
Given $\overline{A B} ≅ \overline{D E}$ and $\overline{C A} ≅ \overline{F D}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SSS? $\overline{B C} ≅ \overline{E F}$
Given $∠ A ≅ ∠ D$ and $\overline{A B} ≅ \overline{D E}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS? $\overline{C A} ≅ \overline{F D}$
Given $\overline{A B} ≅ \overline{D E}$ and $\overline{B C} ≅ \overline{E F}$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS? $∠ B ≅ ∠ E$

Write the congruence statement
The triangles are congruent. Complete the statement:
$△ A C B ≅ △$ $△ F D E$
The triangles are congruent. Complete the statement:
$△ Q P R ≅ △$ $△ K L J$
The triangles are congruent. Complete the statement:
$△ H G I ≅ △$ $△ O M N$

Name the right-triangle congruence rule
The marks show the triangles are congruent. By which rule: HL, LL, HA or LA?HL
Which rule proves the right triangles congruent: HL, LL, HA or LA?HA

How to do these

Which postulate proves the triangles congruent, if any?

Two sides are ticked in each triangle, and the marked angle sits between them.
Side, included angle, side.

The answer is SAS.

Where students go wrong

Reading SSA as SAS. If the marked angle is not between the two marked sides, the pattern proves nothing.

Also called triangle congruence postulates, SSS SAS ASA AAS, hypotenuse leg, CPCTC or congruence statements.

What you can put on this worksheet

SSS, SAS, ASA, AAS, HL, or not enough: Are the triangles congruent? If so, by which postulate? — two triangles with matching marks → ASA
Corresponding parts from a congruence statement: $△ J K L ≅ △ M N O$ . What corresponds to $∠ L$ ? → $∠ O$
Corresponding parts written in x: $△ J K L ≅ △ X Y Z$ , $m ∠ K = {(x + 83)}^{\circ}$ and $m ∠ Y = {(3 x + 69)}^{\circ}$ . Find $x$ . → $7$
What else is needed?: Given $\overline{B C} ≅ \overline{E F}$ and $∠ C ≅ ∠ F$ , what else is needed to prove $△ A B C ≅ △ D E F$ by SAS? → $\overline{C A} ≅ \overline{F D}$
Write the congruence statement: The triangles are congruent. Complete the statement:
$△ X Y Z ≅ △$ — two triangles with their corners named, labeled X, Y, Z, H, G, I → $△ H G I$
Triangles that share a side or meet at a crossing: Name the postulate that shows the triangles are congruent, if there is one. — triangle a b c with segment b d to the base, labeled M, J, K, L → HL
Right triangles: HL, LL, HA, LA: Give the rule (HL, LL, HA or LA) that proves these right triangles congruent. — two right triangles with marks → HA
What else is needed, from a marked drawing (shared sides, crossings, right triangles): What else is needed to prove $△ C A B ≅ △ C A D$ by ASA? — triangle a b c with segment b d to the base, labeled B, C, D, A → $∠ C A B ≅ ∠ C A D$
Matching parts when the triangles share a side: $△ W Y X ≅ △ W Y Z$ . What corresponds to $∠ X W Y$ ? — triangle a b c with segment b d to the base, labeled X, W, Z, Y → $∠ Z W Y$

Questions about these worksheets

Yes. Every congruent triangles sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the congruent triangles questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 9: sss, sas, asa, aas, hl, or not enough, corresponding parts from a congruence statement, corresponding parts written in x, what else is needed?, write the congruence statement, triangles that share a side or meet at a crossing, right triangles: hl, ll, ha, la, what else is needed, from a marked drawing (shared sides, crossings, right triangles) and matching parts when the triangles share a side. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading SSA as SAS. If the marked angle is not between the two marked sides, the pattern proves nothing.

Congruent triangles worksheet

Name the congruence postulate, if any

Name corresponding parts from a congruence statement

Use corresponding parts to find xxx or a part

Name what else is needed

Write the congruence statement

Name the right-triangle congruence rule

Name the congruence postulate, if any

Name corresponding parts from a congruence statement

Use corresponding parts to find xxx or a part

Name what else is needed

Write the congruence statement

Name the right-triangle congruence rule

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these congruent triangles worksheets free?+

Do the congruent triangles worksheets come with an answer key?+

Are these congruent triangles worksheets printable?+

What grade are these congruent triangles worksheets for?+

Can I get a different version of the same congruent triangles worksheet?+

Is this a free alternative to Kuta Software for congruent triangles?+

Can I choose how hard the congruent triangles questions are?+

What kinds of question are on a congruent triangles worksheet?+

What do students get wrong with congruent triangles?+

Use corresponding parts to find $x$ or a part

Use corresponding parts to find $x$ or a part