# PROVING TRIANGLE CONGRUENCE WORKSHEET

## About "Proving triangle congruence worksheet"

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.

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.

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 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.

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 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.

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 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.

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 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.

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 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".

If you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6