All categories

3 years ago

If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then is the triangle isosceles?

Mathematics

1 answer:

Ne4ueva [31]3 years ago

7 0

Answer:

True

Step-by-step explanation:

The perpendicular bisector of the opposite side to the vertex bisects the angle at the vertex into two equal parts and also bisects the triangle into two equal parts.

Let A be the angle at the vertex, then assume that the angle is an isosceles triangle with base angles B.

We need to show that A = 180 - 2B for an isoceles triangle

The perpendicular bisector bisects A into two so the new angle in the vertex one half of the bisected triangle is A/2.

Since this half triangle is a right-angled triangle, the third angle in it is 90.

So, A/2 + B + 90 = 180 (Sum of angles in a triangle)

subtracting 90 from both sides, we have

A/2 + B + 90 - 90 = 180 - 90

A/2 + B = 90

subtracting B from both sides, we have

A/2 + B = 90

A/2 = 90 - B

multiplying through by 2, we have

A = 2(90 - B)

A = 180 - 2B

Since A = 180 - 2B, then our triangle is an isosceles triangle.

You might be interested in

What is the firsf composite number greater than 30 that is not a multiple of 2

natima [27]

35

35 is composite because it has more than one factor

1 3 7 35

35 / 2 is 17.5 so 35 is your answer

4 0

3 years ago

What does a equal in 1/2(a-7)=33?

Dmitriy789 [7]

To find a, you need to isolate/get the variable "a" by itself in the equation:

$\frac{1}{2} (a-7)=33$ Multiply the inverse of 1/2, which is 2, to get rid of the fraction

$(2)\frac{1}{2}(a-7)=(2)33$

a - 7 = 66 Add 7 on both sides to get "a" by itself

a - 7 + 7 = 66 + 7

a = 73

6 0

3 years ago

1. Jordan's washing machine is broken. Since her machine is pretty old, she doesn't want to spend more than $100

ahrayia [7]

Answer:

I think it would be D

Step-by-step explanation:

20 x 3 = 60 60+35= 95 20/4 = 5

4 0

3 years ago

Read 2 more answers

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

Lemur [1.5K]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Do, integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Hence Cardiac output: $F=0.055 L\s$

4 0

2 years ago

Complete this statement: 20 a x 2 + 25 a x + 15 a = 5 a 20 a x 2 + 25 a x + 15 a = 5 a

liubo4ka [24]

Answer:

Step-by-step explanation:

(((22•5ax2) + 25ax) + 15a) - 5 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

20ax2 + 25ax + 15a - 5 =

5 • (4ax2 + 5ax + 3a - 1)

Equation at the end of step 3 :

5 • (4ax2 + 5ax + 3a - 1) = 0

Step 4 :

Equations which are never true :

4.1 Solve : 5 = 0

4 0

3 years ago