Proving triangle congruence worksheet is much useful to the students who would like to practice problems on triangle congruence postulates.

Before we look at the worksheet, let us look at triangle congruence postulates.

1. Side - Side - Side (SSS) Congruence Postulate.

2. Side - Angle - Side (SAS) Congruence Postulate.

3. Angle - Side - Angle (ASA) Congruence Postulate

4. Angle - Angle - Side (AAS) Congruence Postulate

__Be caution :__

SSA and AAA can not be used to test congruent triangles.

**To download "Congruent triangles worksheet pdf", **

Let us practice problems on "congruent triangles worksheet pdf".

**Problem 1 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) AD is common side for both the triangles

(ii) <ABD = <DBC (from the figure)

(iii) Sides BA and BC are congruent (from the figure)

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

Let us look at the next problem on "Proving triangle congruence worksheet"

**Problem 2 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) Sides EF and HJ are congruent. (from the figure)

(ii) Sides FG and JK are congruent.(from the figure)

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 (from the figure)

(ii) Sides NE and RP are congruent (from the figure)

(iii) Sides EM and PQ are congruent (from the figure)

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

But, ASS does not work for congruent triangles.

**Hence, the two triangles are not congruent.**

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**Problem 4 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) Sides TU and WX are congruent (from the figure)

(ii) Sides ST and XV are congruent (from the figure)

(iii) Sides SU and WV are congruent (from the figure)

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

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**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.

(In "congruent triangles worksheet pdf", sometimes we may get problems like this. For this kind of problems, we may have to give answer "Not congruent")

**Problem 6 :**

Check whether two triangles are congruent or not.

**Solution :**

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

(ii) <JKM = <KML

(iii) Sides JK and ML are congruent.

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

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**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**

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**Problem 8 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) <XYZ = <AYB (vertically opposite angles)

(ii) Sides YZ and YB are congruent (from the figure)

(iii) Sides ZX and BA are congruent (from the figure)

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

But, ASS does not work for congruent triangles.

**Hence the two triangles are not congruent.**

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**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**

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**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.(from the figure)

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.

(In "congruent triangles worksheet pdf", sometimes we may get problems like this. For this kind of problems, we may have to give answer "Not congruent")

**Problem 11 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) <X = <Z (right angles)

(ii) Sides AY and WY are congruent.(from the figure)

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

(In "congruent triangles worksheet pdf", sometimes we may get problems like this. For this kind of
problems, we may have to give answer "Not congruent")

**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.(from the figure)

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

But, ASS does not work for congruent triangles.

**Hence the two triangles are not congruent.**

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**Problem 14 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) <M = <Q (right angles)

(ii) Sides MN and QR are congruent (from the figure)

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 (from the figure)

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

(iii) <SVT = <UTV (from the figure)

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

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**Problem 16 :**

Check whether two triangles are congruent or not.

**Solution :**

(ii) <BCE = <DCE (vertically opposite angles)

(ii) <E = <F (from the figure)

(iii) Sides BE and DF are congruent.

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

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**Problem 17 :**

Check whether two triangles are congruent or not.

**Solution :**

(i)<LJK = <HJG (vertically opposite angles)

(ii) Sides KL and GH are congruent (from the figure).

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 (from the figure)

(ii) Sides PM and SQ are congruent (from the figure).

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 (from the figure)

(ii) Sides UV and XY are congruent (from the figure).

(iii) <V = <Y (from the figure)

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

**Let us look at the next problem on "Proving triangle congruence worksheet"**

**Problem 20 :**

Check whether two triangles are congruent or not.

**Solution :**

(i) <G = <D (from the figure)

(ii) <GEF = <DEH (vertically opposite angles)

(ii) Sides HE and FE are congruent (from the figure).

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

After having gone through the stuff given above, we hope that the students would have understood "Proving triangle congruence worksheet".

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