All categories

2 years ago

Which pair of triangles can be proved congruent by the SAS Postulate?

Mathematics

2 answers:

irina [24]2 years ago

8 0

I think its A the first one

qwelly [4]2 years ago

4 0

Answer: $A.\ \triangle{ABX}\cong\triangle{DEX}$

Step-by-step explanation:

In the given picture , we have given that X is the midpoint of $\overline{AD}$ and $\overline{BE}$ .

i.e. AX = XD and BX=XE (1)

Then in $\triangle{ABX}$ and $\triangle{DEX}$ , we have

$\angle{AXB}\cong\angle{EXD}$ [∵ Vertical angles are congruent ]

AX = XD and BX=XE [from (1)]

So by SAS postulate of congruence , we have

$\triangle{ABX}\cong\triangle{DEX}$

You might be interested in

Ahmed an Art dealer earns 25% commission of the dollar value of the art pieces that he sells at the Gallery. Ahmed earns $10,000

Mkey [24]

Answer:

$40,000

Step-by-step explanation:

25% of x = $10,000

0.25x = 10,000

x = 10,000/0.25

x = 40,000

Answer: $40,000

3 0

3 years ago

A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1

Anna11 [10]

Answer:

7.5 ft³/min

Step-by-step explanation:

Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.

Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²

So, V = Ah = 2h = 2(10 - x)

The rate of change of volume is thus

dV/dt = d[2(10 - x)]/dt = -2dx/dt

Since dV/dt = 15 ft³/min,

dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min

Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt

= -dx/dt

= -(-7.5 ft³/min)

= 7.5 ft³/min

And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft

7 0

2 years ago

Find the equation of the line shown.

Ymorist [56]

Answer:

y= -2x+9

Step-by-step explanation:

The equation will be written this way :

y= m*x+c

m is the slope
c is a constant
m =( f(4)-f(2))/(4-2)=(1-5)/2= -4/2 = -2
y = -2x+c
replace x and y by the coordinates of a point to get c
1= -2*4+c
c = 9

y = -2x+9

3 0

2 years ago

Read 2 more answers

A circle's diameter is 4 feet.

Soloha48 [4]

Answer:

Step-by-step explanation:

The formula for cirmference is

C= π2 * r

we're using 3.14 as pi and r = radius.

the radius is always half of the diameter.

So in this case since the diamter is 4, the radius is 2. let's substitute these numbers.

C= 3.14 *2*2 and there your answer is 12.56 which rounded to the nearest tenth is 13.

Hope this helps :)

6 0

1 year ago

The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the follow

mel-nik [20]

Hi there! Hopefully this helps!

----------------------------------------------------------------------------------------------------------

It decreased by 30 cents per week.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The average rate of change is calculated as:

the ratio of the sum of the change in the three weeks divided by the number of weeks. (The number of weeks being 3)

Rate of change = $\frac{-60 -10 -20}{3}$ .

(-60 + -10 + -20 = -90). So, to simplify it:

$\frac{-90}{3}$ = -30

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Incase you are confused:

Since the average rate of change is negative, this means that the stock price has decreased.

3 0

3 years ago