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3 years ago

If two triangles are congruent, which of the following statements must be true?

Mathematics

2 answers:

PSYCHO15rus [73]3 years ago

7 0

Answer:

The correct options are A, B, C and D.

Step-by-step explanation:

A figure said to be congruent if:

Two figures are said to be congruent if they have same size and same shape.

If two figure are congruent that means the corresponding sides will also be congruent.

If two figure are congruent that means the the corresponding angles will also be congruent.

Now consider the provided option.

By the above definition it is clear that all the options are correct.

Hence, the correct options are A, B, C and D.

kobusy [5.1K]3 years ago

3 0

If the two triangles are congruent,
then all four choices are true.

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How many liters of water must be added to 15 liters of 40 % sugar syrup to obtain 30 % sugar syrup?

Ivanshal [37]

Answer:

The amount of water need to be added is 5 liters.

Step-by-step explanation:

Let's "x" be amount of water in (liters) added to 15 liters of 40% of sugar syrup.

Now find the amount of sugar syrup = 40% of 15

= 0.4 × 15

The amount of sugar syrup = 6 Liters

To dilute 30% we need to find amount of water to be added.

So,

30% of (15 + x) = 6

0.3 × (15 + x) = 6

4.5 + 0.3x = 6

0.3x = 6 - 4.5

0.3x = 1.5

Dividing both sides, by 0.3, we get

x = 5

So, the amount of water need to be added is 5 liters.

6 0

3 years ago

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If p=(-3,-2) and q=(1,6) are the endpoints of the diameter of a circle find the equation of the circle

stira [4]

Answer:

The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²

 or 

The equation of the circle x² + 2 x + y² - 4 y = 15

Step-by-step explanation:

Given points end Points are p(-3,-2) and q( 1,6)

The distance of two points formula

P Q = $\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }$

P Q = $\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }$

P Q = $\sqrt{16+64} = \sqrt{80}$

The diameter 'd' = 2 r

2 r = √80

= $\sqrt{16 X 5}$

= $4 \sqrt{5}$

r = 2√5

Mid-point of two end points

$(\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )$

= (-1 ,2)

Mid-point of two end points = center of the circle

(h,k) = (-1 , 2)

The equation of the circle

(x -h )² +(y-k)² = r²

(x -(-1) )² +(y-(2))² = (2(√5))²

x² + 2 x + 1 + y² - 4 y + 4 = 20

x² + 2 x + y² - 4 y = 20 -5

x² + 2 x + y² - 4 y = 15

Final answer:-

The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²

 or 

The equation of the circle x² + 2 x + y² - 4 y = 15

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6.9ft
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strojnjashka [21]

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