Question

# 𝐴𝑃 is perpendicular bisector of 𝐵𝐶.

1. What segment lengths are equal? Explain your reasoning.

2. Find AB.

3. Explain why D is on 𝐴𝑃.

Hint:

- Perpendicular bisector theorem
- According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.

## The correct answer is: 1. equal segments AB = BC, BD = DC and BP = PC 2. AB = 4 units. 3.Yes, D lie on AP.

### Answer:

- Step by step explanation:
- Given:

AB = 6x - 5.

AC = 4x + 1.

BD = 13

DC = 13

AP is perpendicular bisector at BC.

- Step 1:

In

AP is perpendicular bisector.

Therefore, points on AP are equidistant from B and C

So,

AB = AC

6x – 5 = 4x + 1

6x – 4x = 5 + 1

2x = 6

x = 1.5

AB = 6x – 5

AB = 6(1.5) – 5

AB = 9 – 5

AB = 4

- Step 2:

- Given:

BD = 13

DC = 13

Therefore,

Also, BP = PC

DP is perpendicular bisector on BC from D.

Also,

As point D is equidistant from B and C

Therefore, D lies on DP

- Final Answer:

- equal segments AB = BC, BD = DC and BP = PC
- AB = 4 units.
- Yes, D lie on AP.

- Given:

AP is perpendicular bisector at BC.

DP is perpendicular bisector on BC from D.

Also,

As point D is equidistant from B and C

Therefore, D lies on DP

### Related Questions to study

### Identify a monomial.

### Identify a monomial.

### Convert the equation 5x + 4y = 12 into y = mx + c and find its y-intercept.

### Convert the equation 5x + 4y = 12 into y = mx + c and find its y-intercept.

### What must be subtracted from 3x^{2}-5xy -2y^{2}-3 to get 5x^{2}-7xy -3y^{2}+3x

### What must be subtracted from 3x^{2}-5xy -2y^{2}-3 to get 5x^{2}-7xy -3y^{2}+3x

### 𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.

a. What segment lengths in the diagram are equal?

b. Is A on 𝐴𝑃?

### 𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.

a. What segment lengths in the diagram are equal?

b. Is A on 𝐴𝑃?

### Use the square of a binomial to find the value. 56^{2}

### Use the square of a binomial to find the value. 56^{2}

### Is the given conjecture correct? Provide arguments to support your answer.

The product of any two consecutive odd numbers is 1 less than a perfect square.

### Is the given conjecture correct? Provide arguments to support your answer.

The product of any two consecutive odd numbers is 1 less than a perfect square.

### Name the polynomial based on its degree and number of terms.

### Name the polynomial based on its degree and number of terms.

### In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

ii)How many answers did each school get correct in the final round?

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.

¶The standard form of a linear equation in one variable is: ax + b = 0

Where,

The letters 'a' and 'b' are real numbers.

'a' and 'b' are both greater than zero.

### In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

ii)How many answers did each school get correct in the final round?

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.

¶The standard form of a linear equation in one variable is: ax + b = 0

Where,

The letters 'a' and 'b' are real numbers.

'a' and 'b' are both greater than zero.

### Determine the equation of the line that passes through

### Determine the equation of the line that passes through

### Is the given conjecture correct? Provide arguments to support your answer.

The product of any two consecutive even numbers is 1 less than a perfect square

### Is the given conjecture correct? Provide arguments to support your answer.

The product of any two consecutive even numbers is 1 less than a perfect square

### Identify a linear polynomial.

### Identify a linear polynomial.

### Find the value of x. Identify the theorem used to find the answer.

### Find the value of x. Identify the theorem used to find the answer.

### identify a cubic polynomial.

### identify a cubic polynomial.

### Find the value of 𝑚 & 𝑛 to make a true statement.

(𝑚𝑥 + 𝑛𝑦)^{2} = 4𝑥^{2} + 12𝑥𝑦 + 9𝑦^{2}

### Find the value of 𝑚 & 𝑛 to make a true statement.

(𝑚𝑥 + 𝑛𝑦)^{2} = 4𝑥^{2} + 12𝑥𝑦 + 9𝑦^{2}

### 37. In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

i)Which equation models the scoring in the final round and the outcome of the contest

**Different Types of Variables**

### 37. In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

i)Which equation models the scoring in the final round and the outcome of the contest

**Different Types of Variables**