**Triangle Congruence and Similarity Worksheet :**

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

Before look at the worksheet, if you would like to know the stuff related to triangle congruence and similarity,

**Problem 1 :**

Check whether two triangles PQR and WXY are congruent.

**Problem 2 :**

Check whether two triangles PQR and JKL are congruent.

**Problem 3 :**

Check whether two triangles PQR and ABC are congruent.

**Problem 4 :**

Check whether two triangles PQR and CDE are congruent.

**Problem 5 :**

Check whether two triangles PQR and STU are congruent.

**Problem 6 :**

Check whether two triangles PQR and RST are congruent.

**Problem 7 :**

Check whether two triangles ABC and DEF are similar.

**Problem 8 :**

Determine whether the two triangles given below are similar. Justify your answer.

**Problem 9 :**

For what value of x is triangle ABC similar to triangle DEF.

**Problem 10 :**

In the diagram given below, if AC and DE are parallel, find the value of h.

**Problem 1 :**

Check whether two triangles PQR and WXY are congruent.

**Solution :**

(i) Triangle PQR and triangle WXY are right triangles. Because they both have a right angle.

(i) PQ = XY (Hypotenuse).

(ii) PR = WX (Leg)

Hence, the two triangles PQR and WXY are congruent by **Hypotenuse-Leg **theorem.

**Problem 2 :**

Check whether two triangles PQR and JKL are congruent.

**Solution :**

(i) PR = LK (Given)

(ii) ∠R = ∠K (Given)

(i) RQ = JK (Given)

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

**Problem 3 :**

Check whether two triangles PQR and ABC are congruent.

**Solution :**

(i) PQ = BC (Hypotenuse)

(ii) ∠Q = ∠B (Acute angle)

Hence, the two triangles PQR and ABC are congruent by** Hypotenuse-Acute Angle** theorem.

**Problem 4 :**

Check whether two triangles PQR and CDE are congruent.

**Solution :**

(i) ∠R = ∠D (Given)

(ii) PR = ED (Given)

(iii) ∠P = ∠E (Given)

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

**Problem 5 :**

Check whether two triangles PQR and STU are congruent.

**Solution :**

(i) PQ = ST (Given)

(ii) PR = SU (Given)

(iii) QR = TU (Given)

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

**Problem 6 :**

Check whether two triangles PQR and RST are congruent.

**Solution :**

(i) PR = RT (Given)

(ii) ∠SRT = ∠PRQ (Vertical Angles)

(iii) QR = RS (Given)

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

**Problem 7 :**

Check whether two triangles ABC and DEF are similar.

**Solution :**

By Triangle Sum Theorem, in Δ ABC,

∠A + ∠B + ∠C = 180°

21° + 105° + ∠C = 180°

126° + ∠C = 180°

Subtract 126° from both sides.

∠C = 54°

In triangles ABC and DEF, we have

∠A = ∠F = 21°

∠E = ∠C = 54°

Two angles of one triangle are congruent to two angles of another triangle.

By Third Angle Theorem, the third pair of angles must also be congruent.

That is,

∠B = ∠D = 105°

Hence, the triangles ABC and DEF are similar triangles.

**Problem 8 :**

Determine whether the two triangles given below are similar. Justify your answer.

**Solution :**

By Triangle Sum Theorem, in Δ ABC,

∠A + ∠B + ∠C = 180°

60° + ∠B + 79° = 180°

∠B + 139° = 180°

Subtract 139° from both sides.

∠B = 41°

By Triangle Sum Theorem, in Δ DEF,

∠D + ∠E + ∠F = 180°

60° + 42° + ∠F = 180°

102° + ∠F = 180°

Subtract 102° from both sides.

∠F = 78°

In triangles ABC and DEF, we have

∠A = ∠D = 60°

And no more pairs of angles are not congruent.

Hence, the triangles ABC and DEF are not similar triangles.

**Problem 9 :**

For what value of x is triangle ABC similar to triangle DEF.

**Solution :**

Let us assume the given two triangles are similar.

So, the ratio of the corresponding sides must be equal.

By taking the vertices of the triangle in the order (given) ABC and DEF, we have

AB / DE = BC / EF

36 / x = 30 / 15

Take reciprocal on both sides.

x / 36 = 15 / 30

x / 36 = 1 / 2

Multiply both sides by 36

x = 1/2 ⋅ 36

x = 18

Hence the two triangles ABC and DEF are similar for the value of x is 18.

**Problem 10 :**

In the diagram given below, if AC and DE are parallel, find the value of h.

**Solution :**

In the above diagram, we can consider two triangles ABC and DBE.

**Given :** AC and DE are parallel.

The parallel sides AC and DE are cut by the transversal EC.

Then ∠E and ∠C are corresponding angles.

When two parallel lines cut by a transversal, the corresponding angles are congruent.

So, ∠E and ∠C are congruent.

In triangles ABC and DBE, we have

∠E = ∠C

∠B is common angle

Two angles of one triangle are congruent to two angles of another triangle.

By Third Angle Theorem, the third pair of angles must also be congruent.

So, the triangles ABC and DBE are similar triangles.

In similar triangles, the ratio of the corresponding sides are equal.

Then, we have

AB / DB = BC / BE

Plug AB = h, DB = 6, BE = 16 and BC = 56.

h / 6 = 56 / 16

Multiply both sides by 6.

h = 56/16 ⋅ 6

h = 21

Hence, the value of h is 21.

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

Apart from the stuff given on "Triangle congruence and similarity worksheet", if you need any other stuff, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**

HTML Comment Box is loading comments...