**Congruent Triangles on a Coordinate Plane Worksheet :**

**Worksheet given in this section is much useful to the students who would like to practice problems on congruence triangles on the coordinate plane. **

**Problem 1 : **

In the diagram given below, prove that ΔABC ≅ ΔFGH.

**Problem 2 : **

In the diagram given below, prove that ΔABC ≅ ΔDEF.

**Problem 3 : **

In the diagram given below, prove that ΔOPM ≅ ΔMNP.

**Problem 1 : **

In the diagram given below, prove that ΔABC ≅ ΔFGH.

**Solution :**

Because AB = 5 in triangle ABC and FG = 5 in triangle FGH,

AB ≅ FG.

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

AC ≅ FH.

Use the distance formula to find the lengths of BC and GH.

**Length of BC : **

**BC = √[(x₂ - x₁)² + (y₂ - y₁)²]**

**Here (**x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5)

**BC = √[(-4 + 7)² + (5 - 0)²]**

**BC = √[3² + 5²]**

**BC = √[9 + 25]**

**BC = √34**

**Length of GH : **

**GH = √[(x₂ - x₁)² + (y₂ - y₁)²]**

**Here (**x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5)

**GH = √[(6 - 1)² + (5 - 2)²]**

**GH = √[5² + 3²]**

**GH = √[25 + 9]**

**GH = √34**

**Conclusion :**

Because BC = √34 and GH = √34,

BC ≅ GH

All the three pairs of corresponding sides are congruent. By SSS congruence postulate,

ΔABC ≅ ΔFGH

**Problem 2 : **

In the diagram given below, prove that ΔABC ≅ ΔDEF.

From the diagram given above, we have

A(-3, 3), B(0, 1), C(-3, 1), D(0, 6), E(2, 3), F(2, 6)

**Solution :**

Because AC = 2 in triangle ABC and DF = 2 in triangle DEF,

AC ≅ DF.

Because BC = 3 in triangle ABC and EF = 3 in triangle DEF,

BC ≅ EF.

Use the distance formula to find the lengths of BC and GH.

**Length of AB : **

**AB = √[(x₂ - x₁)² + (y₂ - y₁)²]**

**Here (**x₁, y₁) = A(-3, 3) and (x₂, y₂) = B(0, 1)

**AB = √[(0 + 3)² + (1 - 3)²]**

**AB = √[3² + (-2)²]**

**AB = √[9 + 4]**

**AB = √13**

**Length of DE : **

**DE = √[(x₂ - x₁)² + (y₂ - y₁)²]**

**Here (**x₁, y₁) = D(0, 6) and (x₂, y₂) = E(2, 3)

**DE = √[(2 - 0)² + (3 - 6)²]**

**DE = √[2² + (-3)²]**

**DE = √[4 + 9]**

**DE = √13**

**Conclusion :**

Because AB = √13 and DE = √13,

AB ≅ DE

All the three pairs of corresponding sides are congruent. By SSS congruence postulate,

ΔABC ≅ ΔDEF

**Problem 3 : **

In the diagram given below, prove that ΔOPM ≅ ΔMNP.

**Solution :**

PM is the common side for both the triangles OPM and MNP.

Because OP = 6 in triangle OPM and PN = 6 in triangle MNP,

OP ≅ PN.

Use the distance formula to find the lengths of OM and MN.

**Length of OM : **

OM = √[(x₂ - x₁)² + (y₂ - y₁)²]

Here (x₁, y₁) = O(0, 0) and (x₂, y₂) = M(3, 3)

OM = √[(3 - 0)² + (3 - 0)²]

OM = √[3² + 3²]

OM = √[9 + 9]

OM = √18

**Length of MN : **

MN = √[(x₂ - x₁)² + (y₂ - y₁)²]

Here (x₁, y₁) = M(3, 3) and (x₂, y₂) = N(6, 6)

MN = √[(6 - 3)² + (6 - 3)²]

MN = √[3² + 3²]

MN = √[9 + 9]

MN = √18

**Conclusion :**

Because OM = √18 and MN = √18,

OM ≅ MN

All the three pairs of corresponding sides are congruent. By SSS congruence postulate,

ΔOPM ≅ ΔMNP

After having gone through the stuff given above, we hope that the students would have understood, "Congruent triangles on a coordinate plane worksheet".

Apart from the stuff given above, if you want to know more about "Congruent triangles on the coordinate plane", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**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**