Similar Triangles Problems with Answers :
In this section, let us learn, how to solve problems involving the concept similar triangle.
There are three ways to prove that two triangles are similar :
To know more about proving similar triangles, please visit the page "Proving Triangles are Similar".
Example 1 :
P and Q are points on sides AB and AC respectively, of triangle ABC. If AP = 3 cm, PB = 6 cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.
AP/PB = AQ/AC
3/9 = 5/15
1/3 = 1/3
In triangles APQ, and ABC we get
(AP/AB) = (AQ/AC)
∠ A = ∠A
By using SAS criterion ∆ APQ ~ ∆ ABC
(AP/AB) = (Q/AC) = (PQ/BC)
(AP/PB) = (PQ/BC)
PQ/BC = 3/9
PQ/BC = 1/3
3 PQ = BC
BC = 3 PQ
Example 2 :
In triangle ABC, AB = AC and BC = 6 cm. D is a point on the side AC such that AD = 5 cm and CD = 4 cm. Show that triangle BCD and triangle ACB are congruent and hence find BD.
In triangle ABC, AB = AC
(BC/AC) = (CD/CB)
(6/9) = (4/6)
From the triangles ∆ BCD, ∆ ACB we get
(BC/AC) = (CD/CB)
∠ C = ∠ C (Common angle)
By using SAS criterion, we get
∆ BCD ~ ∆ ACB
(BD/AB) = (BC/AC)
Here AB = AC
BD/9 = 6/9
BD = 6 cm
Example 3 :
The points D and E are on the sides AB and AC of triangle ABC respectively, such that DE and BC are parallel. If AB = 3 AD and the area triangle ABC is 72 cm², then find the area of the quadrilateral DBCE.
From the diagram,
the sides DE and BC are parallel and AB = 3 AD
(AD/AB) = 1/3
By taking the two triangles, ∆ ADE and ∆ ABC
∠ ADE = ∠ ABC
∠A = ∠A (Common angle)
By using AA similarity criterion ∆ADE ~ ∆ABC
Area of ∆ ADE/Area of ∆ ABC = AD²/AB²
Area of ∆ ADE/72 = 1/9
Area of ∆ ADE = (1/9) ⋅ 72 = 8 cm
Area of quadrilateral = area of ∆ ABC – Area of ∆ DE
= 72 – 8 = 64 cm²
Therefore the required area of quadrilateral is 64 cm²
After having gone through the stuff given above, we hope that the students would have understood, how to solve problems in similar triangles.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Converting customary units worksheet
Customary units worksheet
Integers and absolute value worksheets
Nature of the roots of a quadratic equation worksheets
Trigonometry heights and distances
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Converting repeating decimals in to fractions