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Kitty [74]
3 years ago
10

Consider the two triangles. Triangles A B C and H G I are shown. Angles A C B and H I G are right angles. The length of side A C

is 15 and the length of side C B is 20. The length of side H I is 12 and the length of I G is 9. To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that

Mathematics
2 answers:
zheka24 [161]3 years ago
8 0

Answer:

Both are similar by SAS similarity.

This SAS similarity is equivalent to the congruence.

Step-by-step explanation:

Step 1:

To prove that ACB and HIG as similar triangles.

We have to look upon the corresponding sides.

SAS= Side angle sides , there the angle must be in between two sides.

\angle ACB = \angle HIG

Lets work on the corresponding sides.

IG/AC = IH/AC

\frac{9}{15} = \frac{12}{20}

Reducing each to lowest form, we divide numerator and denominator by 3 for the 1st fraction and by 4 for the 2nd fraction.

We have

\frac{3}{5} = \frac{3}{5}

Both sides are equal.

So its proved that both are similar with SAS similarity theorem.

garri49 [273]3 years ago
7 0

Answer: C

Step-by-step explanation: I worked it out for you :)

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What is the value of x? assume that the line is tangent to the circle
nekit [7.7K]

Answer:

70°

Step-by-step explanation:

Connect the center of the circle with endpoints of the chord. Let the center of the circle be point O and endpoints of the chord be points A (let point A lie on the tangent line too)and B.

From the figure, central angle AOB has the measure of 220°.

Consider triangle AOB. This triangle is isosceles triangle because OA and OB are both radii. In this triangle the measure of angle AOB is 360° - 220° = 140°.

Angles OAB and OBA are angles adjacent to the base AB, so they are congruent. The sum of the measures of all interior angles in triangle is always 180°, so

m∠OAB + m∠OBA + m∠AOB = 180°

m∠OAB = m∠OBA = 1/2 (180° - 140°)

m∠OAB = 20°

Since drawn line is tangent line, then OA is perpendicular to this tangent line and

x° = 90° - 20°

x° = 70°

4 0
3 years ago
3x+6y=36 and -3x-6y=0​
Anastasy [175]

Answer:

No solution

Step-by-step explanation:

3x + 6y  =36

-3x - 6y =0​

------------------add

0 ≠ 36

No solution

4 0
3 years ago
A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below: The f
Romashka-Z-Leto [24]

The following that could be used to calculate the total volume of grains that can be stored in the silo is π(2 ft)²8 ft + 1/3π(2 ft)²(9.5 ft - 8ft)

To answer the question, we need to know what volume is.

<h3>What is volume?</h3>

This is the capacity of a material or container.

Since the silo is made of a cylindrical and a conical part, we need to find the volume of both parts.

<h3>Volume of cylindrical part.</h3>

So, the volume of the cylindrical part V = πr²h where

  • r = radius of cylidrical part = 4 ft/2 = 2 ft and
  • h = length of cylindrical part = 8 ft.

So, V = πr²h

V = π(2 ft)²8 ft

<h3>Volume of the conical part</h3>

The volume of the conical part is given by V' = 1/3πr²h where

  • r = radius of cone = 2ft and
  • h = height of cone.

Since the entire length of silo is 9.5 ft and length of cylindrical part is 8 ft, then the height of cone is h' = 9.5 ft - 8 ft

So, V' = 1/3πr²h'

V' = 1/3π(2 ft)²(9.5 ft - 8ft)

<h3>Total volume of grains in silo</h3>

The total volume of grains equals the total volume of the silo V" = V + V'

V" = π(2 ft)²8 ft + 1/3π(2 ft)²(9.5 ft - 8ft)

So, the following that could be used to calculate the total volume of grains that can be stored in the silo is π(2 ft)²8 ft + 1/3π(2 ft)²(9.5 ft - 8ft)

Learn more about volume here:

brainly.com/question/25248189

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7 0
2 years ago
Which of the following best describes the solution to the system of equations below?
8090 [49]
The answer is D !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!                                                                               
3 0
3 years ago
Find the circumferences of both circles
serious [3.7K]

Answer:

Blue circle=9π-28.284

Yellow circle=23/2π-36.128

Step-by-step explanation:

the circumfrence is worked out using the equation =pi x diameter

hope this helps ;) xx

4 0
3 years ago
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