Triangles CLASS 10 ICSE CBSE MOST IMPORTANT QUESTIONS WITH SOLUTIONS, TRIANGLES Similarity Important

PQR is a triangle right angled at P and M is a point on QR such that PM perpendicular QR. Show that PM2 = QM × MR.

Triangles Similarity Important and Tricky Question for Exam Class 10 CBSE, NCERT , Ex 6.5 Question 2

Learn Triangles Similarity and entire NCERT Math from class 9th, 10th, 11th and 12th on our website


Let’s now start about the Triangles Similarity:
In the previous standard (class 9th) we have learned about the Triangle Congruency in detail where two triangles of same shape and size are called congruent triangles. In this chapter of similar triangles we will study about the triangles which are of same shape but not necessarily same size. Two figures having the same shape (not necessarily the same size) are called similar figures. We will use this idea to proove many theorems based on triangles similarity and also give a proof of Pythagoras theorem.

In this Similarity of Triangles chapter from class 10th you will learn about

Similar Figures (Basic)
Similarity of Triangles and theorems (Theorem 6.1)
Criteria of similarity of triangles
SSS Theorem
AAA Theorem
SAS Theorem
We will learn about Area of Similar Triangles
Pythagoras Theorem
Solves Questions (All the exercises)

Triangles Similarity Theorem 1

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

Triangles Similarity Theorem AAA
If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar
Triangles Similarity Theorem (SSS)
If in two triangles, corresponding sides are proportional, then their corresponding angles are equal and hence the two triangles are similar

Triangles Similarity Theorem 4
If one angle of a triangle is equal to the one angle of other triangle and the sides including these angles are proportional then the two triangles are similar

Triangles Similarity Theorem 5 (Area)
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Triangles Similarity Theorem 6 (Area)
If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and each other.

Pythagoras Theorem
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Pythagoras Theorem
In a triangle, if square of one side is equal to the sum of other two sides, then angle opposite the first side is right angle

As per the syllabus, you will learn all the topics in my Triangles Similarity Chapter Videos:

Please use this link for the YouTube playlist of Triangles Similarity Class 10th:

This link will get you 67 videos

I have done ex Entire Theorems Proof
Ex 6.1, 6.2, 6.3, 6.4, 6.5,

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Sir explanation is so good...but Plz imrove ur handwriting😅