Areas of Similar Triangles | Finding area using similarity | Ratio of triangle areas

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In this video, we learn how to apply Congruency Rule to solve Problems on Triangles. Use parallel lines concept and triangle similarity theorems to prove/solve problems on solving similar triangles.

Reference book for the above video is

National Council of Educational Research and Training (NCERT) Book for class 10 Subject: Maths

This Video is also refers as CBSE class 10 mathts NCERT Solutions Chapter 6 Triangles

Areas of Similar Triangles

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

00:02 Q1. Let triangle ABC ~ triangle DEF and their areas be, respectively, 64 cm^2 and 121 cm^2. If EF = 15.4 cm, find BC.

00:46 Use conditions of Similar triangles

Measure of corresponding Altitudes are proportional is proportional to the measure of corresponding sides.

01:37 Area of triangles is product of base times height.

04:40 Q2. Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.

05:35 consider ratio of area of triangles

07:22 use AAA similarity criterion

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

08:34 Q3. In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that ar (ABC) AO/ar (DBC) = AO/DO

09:39 construction process to solve problem

10:43 AA similarity criterion

11:30 consider ratio of area of triangles

12:27 Q4. If the areas of two similar triangles are equal, prove that they are congruent.

Q5. D, E and F are respectively the mid-points of sides AB, BC and CA of triangle ABC. Find the ratio of the areas of triangle DEF and triangle ABC.

12:32 Result of Similar Triangles

If two triangles are similar, then (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion).

15:30 Use RHS Congruency

Q6. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

17:00 Know medians of a triangle.

17:20 If two triangles are similar, then (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion).

17:52 The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

20:02 SAS Similarity criteria

21:41 Q7. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

23:21 Apply AAA similarity criterion

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

24:24 Take ratio of the areas of two similar triangles

Tick the correct answer and justify :

25:21 Q8. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of

the areas of triangles ABC and BDE is

(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4

27:15 AA similarity

28:16 9. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio

(A) 2 : 3 (B) 4 : 9 (C) 81 : 16 (D) 16 : 81

28:45 ratio of the areas of two similar triangles

learncbse.in

CBSE solutions for class 10 maths Chapter 6 Triangles Exercise 6.3

CBSE class 10 maths NCERT Solutions chapter 6 Triangles Exercise 6.2 | Thales Theorem

CBSE class 10 maths NCERT Solutions chapter 6 Triangles

Solutions for CBSE class 10 Maths Chapter 6

NCERT solutions for class 10 maths Triangles

NCERT solutions for CBSE class 10 maths Triangles

CBSE class 10 maths Triangles

areas of similar triangles theorem

how to find ratio of triangles

ratio of similar triangles

similar triangles ratio of sides

similar triangles and proportions`

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