Congruence Class 7 Worksheet — Free PDF Download with Answers

Here is a story from a recent parent teacher meeting. A mother told me her daughter kept writing SAS for every congruence question in her school test. When the mother asked why, the girl said her tablet app had given her three SAS examples in a row and she just assumed that was the answer. That is the kind of surface learning that worksheet practice fixes. Paper forces a student to look at each new question afresh.

Congruence is a chapter about precision. You have to match the right sides with the right angles, label the correspondence correctly and cite the correct criterion. There is no room for almost right. Worksheets, with their printed diagrams and space for handwritten reasoning, develop exactly this precision.

When a student writes a congruence proof, they are essentially writing an argument. Each line is a step that must logically follow from the previous. Training this kind of thinking requires slowing down. Apps push you forward with one tap. Paper invites you to pause, check and rewrite.

Worksheets also teach handwriting of geometric notation. The symbol for congruence, the angle symbol, the way sides are marked with dashes — these are small details that matter in exams. Students who only use apps tend to skip them entirely and lose marks for poor presentation.

Finally, worksheet practice is screen free. Half an hour a day with paper and pencil is easier on the eyes and usually more focused than half an hour with a screen.

The worksheet covers every sub topic in the Class 7 congruence chapter.

Sub topics:

* Congruence of plane figures
* Congruence of line segments and angles
* Congruence of triangles
* SSS, SAS, ASA, AAS criteria
* RHS criterion for right triangles
* Identifying corresponding parts
* Applications and proof style questions

Level breakdown:

Total 60 questions with a full answer key.

Revise these points first.

* Congruent figures — Two figures are congruent if they are exactly the same shape and size. One can be placed on top of the other.
* Notation — $\triangle ABC \cong \triangle DEF$ means triangle $ABC$ is congruent to triangle $DEF$. The order of letters shows the correspondence: $A \leftrightarrow D$, $B \leftrightarrow E$, $C \leftrightarrow F$.
* SSS (Side Side Side) — If all three sides of one triangle equal the three sides of another, the triangles are congruent.
* SAS (Side Angle Side) — If two sides and the angle between them in one triangle equal the corresponding parts of another, the triangles are congruent.
* ASA (Angle Side Angle) — If two angles and the included side match, the triangles are congruent.
* AAS (Angle Angle Side) — If two angles and a non included side match, the triangles are congruent.
* RHS (Right Hypotenuse Side) — For right triangles, if the hypotenuse and one leg match, the triangles are congruent.
* SSA is not a congruence criterion — Two sides and a non included angle do not guarantee congruence.

Quick tip: When writing a congruence statement, keep the order of vertices strictly matching. This helps you identify corresponding parts without errors.

Level 1 — Easy

1. State whether two line segments of length $5$ cm each are congruent.
Solution: Yes. Line segments of equal length are congruent.

2. If $\triangle ABC \cong \triangle PQR$, which angle corresponds to $\angle B$?
Solution: $\angle Q$.

3. State the criterion: if all three sides of one triangle equal the three sides of another, the triangles are congruent by ___.
Solution: SSS.

Level 2 — Medium

1. In $\triangle ABC$ and $\triangle DEF$, $AB = DE$, $BC = EF$, $\angle B = \angle E$. Which criterion shows they are congruent?
Solution: SAS.

2. Two triangles have $\angle A = \angle P = 90\degree$, $AB = PQ$, and $AC = PR$. Are they congruent? Give a reason.
Solution: Yes, by SAS (or RHS if we consider the right angle criterion).

3. $\triangle LMN \cong \triangle XYZ$. If $LM = 6$ cm, $XY = ?$
Solution: $XY = 6$ cm (corresponding sides are equal).

Level 3 — Hard

1. In the figure, $AB = AC$ and $AD \perp BC$. Prove that $\triangle ABD \cong \triangle ACD$.
Solution: $AB = AC$ (given). $AD = AD$ (common). $\angle ADB = \angle ADC = 90\degree$ (given $AD \perp BC$). By RHS, $\triangle ABD \cong \triangle ACD$.

2. In $\triangle PQR$ and $\triangle XYZ$, $PQ = XY = 5$ cm, $\angle P = \angle X = 60\degree$, $\angle Q = \angle Y = 70\degree$. By which criterion are they congruent?
Solution: ASA (two angles and the included side).

3. Two triangles have two pairs of sides equal. Are they necessarily congruent? Justify.
Solution: No. For congruence by SAS, the included angle must also be equal. If only two sides are equal with no angle condition, the triangles may differ in shape.

1. Print — Use a clipboard or a clean desk.
2. Warm up — Revise the five criteria by writing them out from memory.
3. Time yourself — 15 minutes for Level 1, 25 for Level 2, 30 for Level 3.
4. Check answers — Use the answer key.
5. Revise mistakes — Redraw the figure and rewrite the proof for every wrong answer.
6. Try again — Next day, retry the wrong ones.

Daily plan: 20 to 25 minutes per day for two weeks.

Weekly revision: Each Sunday, write the five criteria and give one example for each. This keeps them fresh.

1. Wrong order in congruence statement — Writing $\triangle ABC \cong \triangle DFE$ when the correspondence is actually $A \to D$, $B \to E$, $C \to F$. This can cost full marks.

2. Using SSA as a criterion — SSA is not valid for congruence. Students sometimes assume two sides and any angle is enough.

3. Missing the included angle rule — For SAS, the angle must be between the two sides. If it is on a different side, SAS does not apply.

4. Not citing a reason — Congruence questions need you to state the criterion used. Just writing ‘congruent’ without a reason loses marks.

5. Ignoring common sides — In many proofs, two triangles share a side. Students forget to note it. Always add ‘common’ as a reason.

6. Mixing up RHS with SSS — RHS only applies to right triangles. It is not a general criterion for all triangles.

CBSE (NCERT)
Congruence of Triangles is Chapter 7 of NCERT Class 7 maths. Weightage is around 10 to 12 marks. Questions focus on identifying the correct criterion and applying it.

ICSE (Selina / ML Aggarwal)
ICSE covers congruence with more emphasis on proof writing. Students must write each step with a reason. Weightage is around 12 to 15 marks.

IB MYP
IB MYP introduces congruence through transformations (translation, rotation, reflection) rather than criteria. Class 7 IB students may not see SSS, SAS, ASA formally, but they will work with congruent figures visually.

Download the free Class 7 Congruence worksheet:

* Congruence and Symmetry CBSE Worksheet
* Congruence ICSE Worksheet

Online practice:

* Congruence Online — CBSE
* Congruence Online — ICSE

* AI Maths Solver — Upload any congruence problem for a step by step solution.
* Spark Coach — Guided AI tutor.
* Class 7 Maths Complete Guide
* All Worksheets Hub
* Class 7 Formulas

Week 1: Learn the criteria

* Day 1: Read the chapter. Write all five criteria on a flash card.
* Day 2: Level 1 questions 1 to 10.
* Day 3: Level 1 questions 11 to 20.
* Day 4: Level 2 questions 1 to 10 (SSS, SAS).
* Day 5: Level 2 questions 11 to 20 (ASA, AAS, RHS).
* Day 6: Redo all wrong answers.
* Day 7: Rest.

Week 2: Proof writing

* Day 8: Level 3 questions 1 to 5 (basic proofs).
* Day 9: Level 3 questions 6 to 15 (multi step proofs).
* Day 10: Level 3 questions 16 to 20.
* Day 11: Redo wrong Level 3 answers.
* Day 12: Mixed quiz.
* Day 13: Mock test (45 minutes).
* Day 14: Review and summary.

* Class 7 Triangles Worksheet
* Class 7 Lines and Angles Worksheet
* Class 7 Symmetry Worksheet
* Class 7 Visualising Solid Shapes Worksheet
* Class 7 Maths Complete Guide