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∆ ABC with vertices A (–2, 0), B (2, 0) and C (0, 2) is similar to ∆ DEF with vertices D (–4, 0) E (4, 0) and F (0, 4). Is the following statement true or false

Solution:

Given, vertices of ∆ ABC are A(-2, 0) B(2, 0) and C(0, 2)

Vertices of ∆ DEF are D(-4, 0) E(4, 0) and F(0, 4)

We have to check if the triangles ABC and DEF are similar.

By the property of similarity,

The corresponding sides must be in proportion.

So, the side length of each triangle is calculated using the distance formula and verified whether it is proportional.

The distance between two points P (x₁ , y₁) and Q (x₂ , y₂) is

√[(x₂ - x₁)² + (y₂ - y₁)²]

The side length of ∆ ABC are

AB = √[(2 - (-2))²+ (0 - 0)²] = √(4)² = √16 = 4

BC = √[(0 - 2)²+ (2 - 0)²] = √[(2)²+ (2)²] = √(4 + 4) = 2√2

AC = √[(0 - (-2))²+ (2 - 0)²] = √[4 + 4] = 2√2

The side length of ∆ DEF are

DE = √[(4 - (-4))²+ (0 - 0)²] = √(8)² = 8

EF = √[(0 - 4)²+ (4 - 0)²] = √[(-4)²+ (4)²] = √(16 + 16) = √32 = 4√2

DF = √[(0 - (-4))²+ (4 - 0)²] = √(16 + 16) = √32 = 4√2

Now, AB/DE = BC/EF = AC/DF

4/8 = 2√2/4√2 = 2√2/4√2 = 1/2

So, the corresponding sides are in proportion.

Therefore, ∆ ABC ⩬ ∆ DEF

✦ Try This: Determine if ∆ PQR with vertices P (3, 0), Q (3, 0) and R (0, 3) is similar to ∆ DEF with vertices D (-5, 0) E (5, 0) and F (0, 5).

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 1

∆ ABC with vertices A (–2, 0), B (2, 0) and C (0, 2) is similar to ∆ DEF with vertices D (–4, 0) E (4, 0) and F (0, 4). Is the following statement true or false

Summary:

The statement “∆ ABC with vertices A (–2, 0), B (2, 0) and C (0, 2) is similar to ∆ DEF with vertices D (–4, 0) E (4, 0) and F (0, 4)” is true as the corresponding sides are proportional

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