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VikaD [51]
3 years ago
11

Look at the figures. How can you prove the triangles are congruent?

Mathematics
1 answer:
Arada [10]3 years ago
4 0

Answer:

SAS

Step-by-step explanation:

Consider triangles ABC and DEF. In these triangles,

  • AC ≅ FD;
  • AB ≅ DE;
  • ∠A ≅ ∠D (included angle).

Thus, by SAS postulate, triangles ABC and DEF are congruent.

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

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The measure of the​ angle's supplement is 60
Sever21 [200]

Answer:

80°

Step-by-step explanation:

Let the angle be x then four times it's complement plus 60, that is

4(90 - x) + 60 ← is it's supplement

Supplementary angles sum to 180°

Sum the angle and it's supplement and equate to 180

x + 4(90 - x) + 60 = 180 ← distribute and simplify left side

x + 360 - 4x + 60 = 180

- 3x + 420 = 180 ( subtract 420 from both sides )

- 3x = - 240 ( divide both sides by - 3 )

x = 80

The required angle = x = 80°

supplement = 4(90 - 80) + 60 = 4 × 10 + 60 = 40 + 60 = 100°

4 0
2 years ago
For the graph below, what is the cost per bottle?
motikmotik
17.5$ for every 5 bottles refilled. $3.50 for every 1 bottle refilled
7 0
3 years ago
Read 2 more answers
How do I 'Factor the expression 12p+30.' ?
s2008m [1.1K]

Answer:

Grouping and then use the common factor. Therefor the answer is 6(2p+5)

Step-by-step explanation:

I hope this helps.

5 0
3 years ago
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Which figure is the image produced by applying the composition T 0,3 o R0,90 to figure R?
Lyrx [107]

We are given original image R.

It is being translated by (0,3) first and then rotated by a positive angle 90 degrees.

Translation by (0,3) represents (x,y) --> (x, y+3) rule.

Positive 90 degree rotation represents, counterclockwise rotation.

The rule for counterclockwise rotation is (x,y) --> (-y,x).

Therefore, final rule for would be

(x,y) --> ( -y,x+3 )

Let us take a coordinate of R on y-axis as (0,-4).

Now if we apply rule (x,y) --> ( -y,x+3 ) we get

(0,-4)  --> (-(-4), 0+3) = (4,3).

Let us check the figure with coordinate (4,3).

We can clearly see that Figure H has transformed coordinate (4,3).

<h3>Therefore, correct option is first option A. figure H.</h3>
8 0
3 years ago
What is the minimum number of angles required to determine the Cartesian components of a 3D vector and why?
Reika [66]

Answer: 3

Step-by-step explanation:

The 3D vector consists of 3 axes, let's say x, y and z.

Now, a vector P lies in all of them.

So, the angle it makes with x axis is α

The angle it makes with y axis is β

The angle it makes with z axis is γ

So, to determine the Cartesian components or to resolve the vector into it's Cartesian components we need 3 angles with each axis.

4 0
3 years ago
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