**Proving Triangle Congruence Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on triangle congruence postulates.

Before look at the worksheet, if you know the stuff related to triangle congruence postulates and theorem,

**Problem 1 :**

Check whether two triangles are congruent or not.

**Problem 2 :**

Check whether two triangles are congruent or not.

**Problem 3 :**

Check whether two triangles are congruent or not.

**Problem 4 :**

Check whether two triangles are congruent or not.

**Problem 5 :**

Check whether two triangles are congruent or not.

**Problem 6 :**

Check whether two triangles are congruent or not.

**Problem 7 :**

Check whether two triangles are congruent or not.

**Problem 8 :**

Check whether two triangles are congruent or not.

**Problem 9 :**

Check whether two triangles are congruent or not.

**Problem 10 :**

Check whether two triangles are congruent or not.

**Problem 11 :**

Check whether two triangles are congruent or not.

**Problem 12 :**

Check whether two triangles are congruent or not.

**Problem 13 :**

Check whether two triangles are congruent or not.

**Problem 14 :**

Check whether two triangles are congruent or not.

**Problem 15 :**

Check whether two triangles are congruent or not.

**Problem 16 :**

Check whether two triangles are congruent or not.

**Problem 17 :**

Check whether two triangles are congruent or not.

**Problem 18 :**

Check whether two triangles are congruent or not.

**Problem 19 :**

Check whether two triangles are congruent or not.

**Problem 20 :**

Check whether two triangles are congruent or not.

**Problem 1 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) AD is common side for both the triangles.

(ii) ∠ABD = ∠DBC (Given).

(iii) Sides BA and BC are congruent (Given).

Hence, the two triangles are congruent by **SAS** postulate.

**Problem 2 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) Sides EF and HJ are congruent (Given).

(ii) Sides FG and JK are congruent (Given).

That's all the information we can have from the given figure.

Since the information given in the figure is insufficient, we can not conclude whether the two triangles are congruent or not.

**Problem 3 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠N = ∠R (Given).

(ii) Sides NE and RP are congruent (Given).

(iii) Sides EM and PQ are congruent (Given).

From the above three points, we get **ASS**.

But, ASS does not work for congruent triangles.

Hence, the two triangles are not congruent.

**Problem 4 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) Sides TU and WX are congruent (Given).

(ii) Sides ST and XV are congruent (Given).

(iii) Sides SU and WV are congruent (Given).

Hence, the two triangles are congruent by **SSS** postulate.

**Problem 5 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) YA is common side for both the triangles.

(ii) ∠YAB = ∠YAZ (Right angles).

That's all the information we can have from the given figure.

Since the information given in the figure is insufficient, we can not conclude whether the two triangles are congruent or not.

**Problem 6 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) MK is common side of both the triangles..

(ii) ∠JKM = ∠KML (Given).

(iii) Sides JK and ML are congruent.

Hence, the two triangles are congruent by **SAS** postulate.

**Problem 7 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) PR is common side for both the triangles.

(ii) Sides PN and PQ are congruent.

(iii) Sides NR and QR are congruent.

Hence, the two triangles are congruent by **SSS** postulate.

**Problem 8 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠XYZ = ∠AYB (Vertically opposite angles).

(ii) Sides YZ and YB are congruent (Given).

(iii) Sides ZX and BA are congruent (Given).

From the above three points, we get **ASS.**

But, ASS does not work for congruent triangles.

Hence the two triangles are not congruent.

**Problem 9 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) GE is common side for both the triangles.

(ii) Sides DE and GF are congruent.

(iii) Sides DG and EF are congruent.

Hence, the two triangles are congruent by **SSS** postulate.

**Problem 10 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) VT is common side for both the triangles.

(ii) Sides ST and VU are congruent (Given).

That's all the information we can have from the given figure.

Since the information given in the figure is insufficient, we can not conclude whether the two triangles are congruent or not.

**Problem 11 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠X = ∠Z (Right angles).

(ii) Sides AY and WY are congruent(Given).

That's all the information we can have from the given figure.

**Problem 12 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠J = ∠H (Right angles).

(ii) GK is common side for both the triangles.

That's all the information we can have from the given figure.

**Problem 13 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠PLK = ∠PLM (Right angles).

(ii) PL is common side for both the triangles.

(iii) Sides PK and PM are congruent (Given).

From the above three points, we get **ASS.**

But, ASS does not work for congruent triangles.

Hence the two triangles are not congruent.

**Problem 14 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠M = ∠Q (Given : Right angles).

(ii) Sides MN and QR are congruent (Given).

That's all the information we can have from the given figure.

**Problem 15 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠STV = ∠UVT (Given).

(ii) TV is common side for both the triangles.

(iii) ∠SVT = ∠UTV (Given).

Hence, the two triangles are congruent by **ASA** postulate.

**Problem 16 :**

Check whether two triangles are congruent or not.

**Solution :**

(ii) ∠BCE = ∠DCE (Vertically opposite angles).

(ii) ∠E = ∠F (Given).

(iii) Sides BE and DF are congruent.

Hence, the two triangles are congruent by **AAS** postulate.

**Problem 17 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠LJK = ∠HJG (Vertically opposite angles).

(ii) Sides KL and GH are congruent (Given).

That's all the information we can have from the given figure.

**Problem 18 :**

Check whether two triangles are congruent or not.

(i) ∠M = ∠Q (Given).

(ii) Sides PM and SQ are congruent (Given).

That's all the information we can have from the given figure.

**Problem 19 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠U = ∠X (Given).

(ii) Sides UV and XY are congruent (Given).

(iii) ∠V = ∠Y (Given).

Hence, the two triangles are congruent by **ASA** postulate.

**Problem 20 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) ∠G = ∠D (Given).

(ii) ∠GEF = ∠DEH (Vertically opposite angles).

(ii) Sides HE and FE are congruent (Given).

Hence, the two triangles are congruent by **AAS** postulate.

If you would like to download congruent triangles worksheet as pdf document,

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