Maths-

General

Easy

Question

# Determine if the given conjecture is true or not. Give a counterexample if it is false.

Given: ∠𝑃 𝑎𝑛𝑑 ∠𝑄 are complementary. ∠𝑄 𝑎𝑛𝑑 ∠𝑅 are complementary.

Conjecture: ∠𝑃 ≅ ∠𝑅

## The correct answer is: the given conjecture is true

### We have given that

∠𝑃 𝑎𝑛𝑑 ∠𝑄 are complementary.

∠𝑄 𝑎𝑛𝑑 ∠𝑅 are complementary.

Which means ∠𝑃 + ∠𝑄 = 90

And ∠𝑄 + ∠𝑅 = 90

If we subtract ∠𝑄 from both sides of both equations we get,

∠P =90 - ∠𝑄

∠R = 90 - ∠𝑄

If we compare RHS of the both obtained equations

We can say that

∠𝑃 ≅ ∠𝑅

Therefore, the given conjecture is true.

Which means ∠𝑃 + ∠𝑄 = 90

And ∠𝑄 + ∠𝑅 = 90

If we subtract ∠𝑄 from both sides of both equations we get,

If we compare RHS of the both obtained equations

We can say that

Therefore, the given conjecture is true.

### Related Questions to study

Maths-

### A plate of 3 cm thick, 9 cm broad, and 27 m long is melted into a cube. find the difference in surface area of the two solids correct to the nearest whole number.

### A plate of 3 cm thick, 9 cm broad, and 27 m long is melted into a cube. find the difference in surface area of the two solids correct to the nearest whole number.

Maths-General

Maths-

### Which number is next in the sequence?

35, 85, 135, 185, __

### Which number is next in the sequence?

35, 85, 135, 185, __

Maths-General

General

### A cuboidal water tank is 6m long , 5m wide and 4.5 m deep.

How many litres of water can it hold ?

### A cuboidal water tank is 6m long , 5m wide and 4.5 m deep.

How many litres of water can it hold ?

GeneralGeneral

Maths-

### Show the conjecture is false by finding a counterexample.

Two supplementary angles form a linear pair.

### Show the conjecture is false by finding a counterexample.

Two supplementary angles form a linear pair.

Maths-General

Maths-

### Show the conjecture is false by finding a counterexample.

Two adjacent angles always form a linear pair

### Show the conjecture is false by finding a counterexample.

Two adjacent angles always form a linear pair

Maths-General

Maths-

### A cubical tank 50 cm in length and 36 cm in breadth contain water. A cube of x cm edge is dropped into it and fully immersed. If the rise in water level is 15 cm, solve for x. and hence find the T.S.A of the cubical tank

### A cubical tank 50 cm in length and 36 cm in breadth contain water. A cube of x cm edge is dropped into it and fully immersed. If the rise in water level is 15 cm, solve for x. and hence find the T.S.A of the cubical tank

Maths-General

Maths-

### Show the conjecture is false by finding a counterexample.

If the product of two numbers is even, then the two numbers must be even.

### Show the conjecture is false by finding a counterexample.

If the product of two numbers is even, then the two numbers must be even.

Maths-General

Maths-

### Show the conjecture is false by finding a counterexample.

If a + b = 0, then a = b = 0.

### Show the conjecture is false by finding a counterexample.

If a + b = 0, then a = b = 0.

Maths-General

Maths-

### calculate the surface area of a cube and volume of a cube with the given diagonal length of 15cm

### calculate the surface area of a cube and volume of a cube with the given diagonal length of 15cm

Maths-General

Maths-

### Show the conjecture is false by finding a counterexample.

If the product of two numbers is positive, then the two numbers must both be positive.

### Show the conjecture is false by finding a counterexample.

If the product of two numbers is positive, then the two numbers must both be positive.

Maths-General

Maths-

### Show the conjecture is false by finding a counterexample.

The square root of any positive integer x is always less than x.

### Show the conjecture is false by finding a counterexample.

The square root of any positive integer x is always less than x.

Maths-General

Maths-

### Show the conjecture is false by finding a counterexample.

All prime numbers are odd.

### Show the conjecture is false by finding a counterexample.

All prime numbers are odd.

Maths-General

Maths-

### Complete the conjecture.

The sum of the first n odd positive integers is ____.

### Complete the conjecture.

The sum of the first n odd positive integers is ____.

Maths-General

Maths-

### A square is drawn with the length of the side equal to the diagonal of the cube. if the square area is 72075 cm^{2}, then find the side of the cube?

### A square is drawn with the length of the side equal to the diagonal of the cube. if the square area is 72075 cm^{2}, then find the side of the cube?

Maths-General

Maths-

### What are all the possible values of b for which is it factorable using only integer coefficients and constant?

### What are all the possible values of b for which is it factorable using only integer coefficients and constant?

Maths-General