Topics
Real Numbers
Number Systems
Algebra
Polynomials
Coordinate Geometry
Pair of Linear Equations in Two Variables
- Pair of Linear Equations in Two Variables
- Graphical Method with Different Cases of Solution
- Algebraic Methods of Solving a Pair of Linear Equations
- Substitution Method
- Elimination Method
Geometry
Quadratic Equations
Trigonometry
Arithmetic Progressions
Mensuration
Coordinate Geometry
Statistics and Probability
Triangles
Circles
Introduction to Trigonometry
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability
CISCE: Class 10
Key Points: Criteria for Similarity of Triangles
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AA / AAA → two angles equal
-
SAS → included angle equal + sides proportional
-
SSS → all sides proportional
Example
In triangles ABC and PQR, AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm, QR = 5 cm and PR = 3.5 cm. Examine whether the two triangles are congruent or not. If yes, write the congruence relation in symbolic form.
Here,
AB = PR (= 3.5 cm),
BC = PQ (= 7.1 cm) and
AC = QR (= 5 cm)
This shows that the three sides of one triangle are equal to the three sides of the other triangle. So, by SSS congruence rule, the two triangles are congruent. From the above three equality relations, it can be easily seen that A ↔ R, B ↔ P, and C ↔ Q.
So, we have ∆ ABC ≅ ∆ RPQ.
Example
In Fig, AD = CD and AB = CB.
(i) State the three pairs of equal parts in ∆ABD and ∆CBD.
(ii) Is ∆ABD ≅ ∆CBD? Why or why not?
(iii) Does BD bisect ∠ABC? Give reasons.
(i) In ∆ABD and ∆CBD, the three pairs of equal parts are as given below:
AB =CB.....................(Given)
AD =CD...................(Given) and
BD =BD....................(Common in both)
(ii) From (i) above, ∆ABD ≅ ∆CBD.............(By SSS congruence rule)
(iii) ∠ABD = ∠CBD..................(Corresponding parts of congruent triangles)
So, BD bisects ∠ABC.
