**How to prove two triangles are similar ? **

If two triangles are similar, then the measures of their corresponding sides are proportional, and the measures of their corresponding angles are equal.

If ΔABC ∼ ΔDEF,

then AB/DE = BC/EF = AC/DF

Let us see some example problems to understand how to prove two triangles are similar.

**Example 1 :**

Determine whether each pair of triangles is similar. Justify your answer.

**Solution :**

The angles BAC and DFE are congruent.To prove the above triangles are similar, we need to prove one more pairs of angles are equal.

To check whether the angles BCA and DEF are equal, let us find the measure of angle BCA from triangle ABC.

∠BAC + ∠ABC + ∠BCA = 180

21 + 105 + ∠BCA = 180

126 + ∠BCA = 180

∠BCA = 180 - 126

∠BCA = 54^{0}

∠BCA = ∠DEF

In triangle ABC ∠BAC ∠BCA |
In triangle DEF ∠DFE ∠DEF |

Hence the triangles ABC and DEF are similar.

**Example 2 :**

Determine whether each pair of triangles is similar. Justify your answer.

**Solution :**

The angles ∠ACB and ∠FDE are congruent.To prove the above triangles are similar, we need to prove one more pairs of angles are equal.

To check whether the angles ABC and DEF are equal, let us find the measure of angle ABC from triangle ABC.

∠ABC + ∠BAC + ∠ACB = 180

∠ABC + 79 + 60 = 180

∠ABC + 139 = 180

∠ABC = 180 - 139

∠ABC = 41

∠ABC ≠ ∠DEF

Hence the above triangles ABC and DEF are not similar.

**Example 3 :**

Determine whether each pair of triangles is similar. Justify your answer.

**Solution :**

To check whether the above triangles are similar, we need to find the missing angles of triangle ABC.

∠ABC + ∠BAC + ∠ACB = 180

84 + ∠BAC + ∠ACB = 180

2∠BAC = 180 - 84

2∠BAC = 96

∠BAC = 96/2

∠BAC = 48 = ∠ACB

The corresponding angles of BAC and DEF are not same. Hence the above triangles are not similar.

After having gone through the stuff given above, we hope that the students would have understood "How to prove two triangles similar".

Apart from the stuff given above, if you want to know more about "How to prove two triangles similar", Please click here

Apart from the stuff given on this web page, if you need any other stuff in math, 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**