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2 years ago

Which congruence theorems can be used to prove ΔEFG ≅ ΔJHG? Select two options.

Mathematics

2 answers:

mezya [45]2 years ago

5 0

<h2><u><em>Answer: </em></u></h2><h2><u><em> </em></u></h2>

ASA and AAS

<h2><u><em>Step-by-step explanation: </em></u></h2>

We do not know if these are right triangles; therefore we cannot use HL to prove congruence.

We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.

We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.

Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

choli [55]2 years ago

4 0

Answer:

ASA

Step-by-step explanation:

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A research submarine descends 65 meters per minutes to a depth of 4485 m, conducts experiments, and then ascends at a rate of 65

sukhopar [10]

Answer:

Step-by-step explanation:

speed =65m/mins = 65/60 = 1.083m/s

Time taken to go down,

t = 4485/1.083

= 4141.37 s

Total time gotten = 12 hrs = 12*60*60

= 43200s

Amount of time left to conduct experiment

= 43200-4141.37

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= 39058.63/3600

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7 0

2 years ago

Read 2 more answers

The quotient of 38 times a number and -4

nikdorinn [45]

Answer:

140y

Step-by-step explanation:

35 times a number times -4 is 35×y×(-4) which is -140y

4 0

1 year ago

Gary used landscape timbers to create a border around a garden shaped like a right triangle. The longest two timbers he used are

Cloud [144]

Answer:

9 feet

Step-by-step explanation:

Given:

The border of the garden is a right angled triangle.

Two lengths are given as 12 ft and 15 ft.

Let the length of the shortest timber be 'x' feet.

Now, in a right angled triangle, the longest length is called the hypotenuse.

As 15 feet is the largest length, it is the hypotenuse of the triangle. Now, applying Pythagoras theorem, we get:

$(Leg1)^2+(Leg2)^2=(Hypotenuse)^2\\x^2+12^2=15^2\\x^2+144=225\\x^2=225-144\\x^2=81\\x=\pm \sqrt{81}=\pm 9$

The negative value is neglected as length can never be negative.

Therefore, the length of the shortest timber is 9 feet.

8 0

2 years ago

If r is the midpoint of qs rs=2x-4, st= 4x-1 and rt = 8x-43 find qs

sammy [17]

Answer:

$QS=68\ units$

Step-by-step explanation:

step 1

Find the value of x

we know that

r is the midpoint of qs

QR=RS

QS=QR+RS------> QS=2RS -----> equation A

RT=RS+ST ----> equation B

see the attached figure to better understand the problem

Substitute the given values in the equation B and solve for x

$8x-43=(2x-4)+(4x-1)$

$8x-43=6x-5$

$8x-6x=43-5$

$2x=38$

$x=19$

step 2

Find the value of RS

$RS=2x-4$

substitute the value of x

$RS=2(19)-4$

$RS=34\ units$

step 3

Find the value of QS

Remember equation A

QS=2RS

$QS=2(34)=68\ units$

6 0

2 years ago

Point H is the circumcenter of triangle DEF. Which must be true? Check all that apply. Point H is the center of the circle that

Dmitrij [34]

The circumcenter of a triangle is the intersection of the perpendicular bisectors.It is the center of the triangle's circumcircle. And a circumcircle is the circumscribed circle of the triangle. This unique circle passes through each of the triangle's three vertices. According to these definitions the following statement is true:
Point H is the center of the circle that passes through points D, E, and F.

5 0

2 years ago