HOW TO FIND THE MISSING SIDES OF SIMILAR TRIANGLES
In geometry two triangles are similar if and only if corresponding angles are congruent and the lengths of corresponding sides are proportional.
Let us look at some examples to understand how to find the lengths of missing sides in similar triangles.
Example 1 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
k = 9, n = 6, o = 8, p = 4
Solution :
Because the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
k = 9, n = 6, o = 8, p = 4
m/4 = 9/6 = l/8
|
m/4 = 9/6 m = 36/6 m = 6 |
l/8 = 9/6 l = 72/6 l = 12 |
Example 2 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
k = 24, l = 30, m = 15, n = 16
Solution :
Because the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
k = 24, l = 30, m = 15, n = 16
15/p = 24/16 = 30/o
|
15/p = 24/16 p/15 = 16/14 p = 240/24 p = 10 |
30/o = 24/16 o/30 = 16/24 o = 480/24 o = 20 |
Example 3 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
m = 11, p = 6, n = 5, o = 4
Solution :
Because the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
m = 11, p = 6, n = 5, o = 4
11/6 = k/5 = l/4
|
11/6 = k/5 55/6 = k 9.16 = k |
l/4 = 11/6 l = 44/ 6 l = 7.33 |
Example 4 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
k = 16, l = 13, m = 12, o = 7
Solution :
Because the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
k = 16, l = 13, m = 12, o = 7
12/p = 16/n = 13/7
|
12/p = 13/7 p/12 = 7/13 p = 12(7) / 13 p = 84/13 p = 6.46 |
16/n = 13/7 n/16 = 7/13 n = 7(16)/13 n = 112/13 n = 8.62 |
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the 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
Trigonometry 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
Recent Articles
-
3 Ways to Pass Your Math Test with Success
Dec 04, 21 06:58 AM
3 Ways to Pass Your Math Test with Success
-
Free Math Worksheets Pdf
Dec 04, 21 06:52 AM
Free Math Worksheets Pdf
-
SHSAT Practice Questions With Answers
Dec 04, 21 06:26 AM
SHSAT Practice Questions With Answers
