X + 8 + =18 whats the value of x

The answer has to be a geometric proof. Thank you!

Mariulka [41]

Given data:

The given triangle in which AD is on perpendicular bisector on BC.

In triangle ABD and ACD.

$\begin{gathered} \angle ADB=\angle\text{ADC}=90^{\circ} \\ BD=CD(\text{given)} \\ AD=AD\text{ (common)} \\ \Delta ABD\cong\Delta ACD(\text{SAS)} \end{gathered}$

Simmilary triangle BED and triangle CED.

$\begin{gathered} \angle BDE=\angle CDE \\ BD=CD \\ ED=ED \\ \Delta BED\cong\Delta CED(SAS) \end{gathered}$

The fisr expression can be written as,

$\begin{gathered} \Delta ABD\cong\Delta ACD \\ \Delta\text{ABE}+\Delta BED\cong\Delta ACE+\Delta\text{CED} \end{gathered}$

Substitute CED in place of BED.

$\begin{gathered} \Delta ABE+\Delta CED\cong\Delta ACE+\Delta CED \\ \Delta ABE\cong\Delta ACE \end{gathered}$

Thus, the triangle ABE is congruent to trriangle ACE.

7 0

1 year ago

The two triangles are similar.<br> What is the value of x?<br> Enter your answer in the box.<br> X=

fomenos

Answer:

Step-by-step explanation:

In similar triangles, the corresponding sides are in same proportion.

$\sf \dfrac{4x}{3x+1}=\dfrac{15}{12}$

Cross multiply,

4x*12 = 15*(3x + 1)

48x = 15*3x + 15*1

48x = 45x + 15

48x -45x = 15

3x = 15

x = 15/3

x = 5

8 0

2 years ago

( please help !! )

sergij07 [2.7K]

Answer:

A. Circular base of the bucket

B. Bucket

Step-by-step explanation:

We are given that,

1. The dimensions of the rectangular prism are,

Length = 2 feet, Width = 3 feet and Height = 5 feet.

So, we have,

Area of the rectangular base = $Length\times Width$

i.e. Area of the rectangular base = $2\times 3$

i.e. Area of the rectangular base = 6 feet²

Also, we have,

Volume of the prism = $whl$

i.e. Volume of the prism = $3\times 5\times 2$

i.e. Volume of the prism = 30 feet³

2. The dimensions of the cylinder are given as,

Diameter = 3 feet i.e Radius = $\frac{3}{2}$ = 1.5 feet

Height = 5 feet

Then, we have,

Area of the circular base = $\pi r^2$

i.e. Area of the circular base = $\pi (1.5)^2$

i.e. Area of the circular base = $2.25\pi$

i.e. Area of the circular base = 7.07 feet²

Also, we have,

Volume of the cylinder = $\pi r^{2}h$

i.e. Volume of the cylinder = $\pi (1.5)^{2}\times 5$

i.e. Volume of the cylinder = $\pi 2.25\times 5$

i.e. Volume of the cylinder = $11.25\pi$

i.e. Volume of the cylinder = 35.34 feet³

PART A: Since we have,

Area of the rectangular base = 6 feet² < 7.07 feet² = Area of the circular base

Hence, the circular base of the bucket is larger in area.

PART B: We have,

Volume of the prism = 30 feet³ < 35.34 feet³ = Volume of the cylinder

Hence, the bucket is larger in volume.

3 0

3 years ago

BAD is congruent to BCD by <br> the

scoundrel [369]

AB is congruent to BC

6 0

4 years ago

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

AnnyKZ [126]

Answer: D

Step-by-step explanation:

I got (-7,0) for the focus & Origin: (0,0)

3 0

3 years ago