### CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

# SIMILARITY OF TRIANGLES  CLASS 10 CHAPTER 6

Similarity of Triangles, SSS Similarity Rule, SAS Similarity Rule, AAA Similarity Rule, AA Similarity Rule, B.P.T. Pythagoras Theorem

Similar figures:-
Two figures which looks same but not necessarily having the same size are called similar figures.

# Similarity of Triangles

Two triangles are similar if their corresponding sides are proportional and angles are equal.
For example :- Two same photos of different size are similar to each other.
• All equilateral triangles are similar.
• All squares are similar to each other.
• All congruent figures are similar to each other, but all similar figures may or may not be similar.
• Similarity of two figures are shown by using the symbol  "〜"
• A polygon is said to be similar if its corresponding angles are equal and sides are proportional.
Similarity conditions of triangles :-
Triangles can be made similar with the help of four conditions, SSS, SAS, AAA, AA conditions
Explanation of all conditions

Side – Side - Side (SSS) Similarity Rule :-

Two triangles are said to be similar by SSS similarity rule  if their corresponding sides are proportional.

Side – Angle - Side (SAS) Similarity Rule :-

Two triangles are said to be similar by SAS similarity rule if their two corresponding sides are proportional to each other and corresponding angles included between the proportional sides are equal.

Angle – Angle - Angle (AAA) Similarity Rule :-

Two triangles are said to be similar by AAA similarity rule If three angles of one triangle are equal to the  three angles of other triangle.
Angle – Angle Similarity Rule :-

Two triangles are said to be similar by AA similarity rule  If two angles of one triangle are equal to the two angles of other triangle.

Basic Proportionality Theorem (B.P.T.) or Thales Theorem :-

If a line is drawn parallel to one side of triangle to intersect the other two sides at two distinct points, then other two sides are divided into same ratio.

Theorem on Area of two similar triangles:-

Ratio of areas of two similar triangles is equal to the ratio of square of their corresponding sides.

Pythagoras Theorem:-

In right angled triangle the square of the longest side is equal to the sum of square of the other two sides.

Converse of Pythagoras theorem :-

If square of one side of a triangle is equal to the sum of square of the other two sides then angle opposite to the longest side is equal to the right angle.

SIMILARITY OF TRIANGLES

Important Notes:-

• If two triangles are similar then their corresponding sides, medians, altitudes and perimeters are proportional to each other.

• If two triangles are similar then ratio of areas of two similar triangle is equal to the ratio of square of their sides, their medians, their altitudes.

• In a right angled triangle if a perpendicular is drawn from the right angle to the hypotenuse then triangles on either side of the perpendicular is similar to each other and to the whole triangle.

Important Result :

Internal bisector of angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.    In Triangle ABC, if AD is the bisector of ∠A then $\frac{AB}{AC}=\frac{BD}{DC}$

SIMILARITY OF TRIANGLES

🙏