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hodyreva [135]
2 years ago
9

Can you help me write proofs for these, PLEASE!!!

Mathematics
1 answer:
brilliants [131]2 years ago
4 0

Exterior angle theorem and properties of the isosceles triangles are used

prove the specified relations.

Correct responses:

9. ΔPAT ~ ΔPTB by AA similarity postulate

15. \overleftrightarrow{HM}║\overleftrightarrow{JK} by basic proportionality theorem

<h3>Detailed methods used to prove response</h3>

9. A two column proof is presented as follows;

Statement {}                                     Reasons

1. ∠PTA = ∠B {}                           1.  Given

2. ∠PAT = ∠ATB + ∠B  {}           2.  Exterior angle of a triangle theorem

3. ∠BTP = ∠ATB + ∠PTA {}        3   Angle addition postulate

4. ∠BTP = ∠ATP + ∠B {}             4.  Substitution property of equality

5. ∠PAT = ∠BTP {}                      5.  Substitution property

6. ΔPAT ~ ΔPTB {}                      6. AA similarity postulate

The Angle-Angle, AA, similarity postulate states that two triangles are similar if two angles in one triangle are each equal to two angles in the other triangle.

15. A two column proof is presented as follows;

Statement                        {}                         Reasons

\displaystyle 1. \hspace{0.3 cm} \frac{GJ}{HK}  = \frac{GK}{GM}                            {}          1.  Given

2. ∠1 ≅ ∠G                          {}                   2. Given

3. ΔKHG is an isosceles triangle{}         3. Definition

4. HK = HG {}                                            4. Legs of an isosceles triangle

\displaystyle 5. \hspace{0.3 cm} \frac{GJ}{HG} = \frac{GK}{GM}              {}                         5. Substitution property

6. \overleftrightarrow {HM} ║ \overleftrightarrow{JK}                      {}                    6. BPT, Basic Proportionality Theorem

Basic Proportionality Theorem, BPT, states that if a line parallel to one of the sides of a triangle, intersects the other two sides, then the line divides the other two sides in the same proportion.

Learn more about basic proportionality theorem, AA similarity postulate here:

brainly.com/question/14417137

brainly.com/question/17003791

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Solve for x. round to the nearest hundredth if necessary.
iris [78.8K]

Answer: x=11.47

Step-by-step explanation:

Given the angle of 55 degrees, you know that the adjacent side is "x" and the length of the hypotenuse is 20.

Therefore, you need to remember the following identity:

cos\alpha=\frac{adjacent}{hypotenuse}

Then, knowing that:

\alpha=55\°\\adjacent=x\\hypotenuse=20

 You need to substitute these values intocos\alpha=\frac{adjacent}{hypotenuse}:

 cos(55\°)=\frac{x}{20}

Now, you can solve for "x":

20*cos(55\°)=x\\x=11.471

Rounded to the nearest hundreth:

x=11.47

6 0
3 years ago
What is the mass of 2.5 moles of carbon dioxide?
GarryVolchara [31]

Answer:

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CO2 molecule is made up of Carbon (atomic mass =12) and oxygen (atomic mass=16).

So first finding the mass of 1 molecule of CO2 which is equals to

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Now 1 molecule of CO2 has mass 44 amu so mass of 1 mole CO2 will be 44 grams.( 1 a.m.u.=1.6729*10^-33 grams. 1 mole = 6.022*10^23, so 44 a.m.u.=73.6076*10^-33 grams approx. For one mole CO2, 73.6076*10^-33*6.022*10^23 which is approximately equals to 44 grams. )

1 mole CO2= 44grams, so 2.5 moles = 44*2.5= 110 grams

So our answer is 110 grams.

lowkey hope this helped you, good luck whatever you need it for Imaooo

3 0
3 years ago
If 11 is subtracted from twice a number the answer is 7. Find the number?
KonstantinChe [14]
Answer:
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Solution:

Write it in an algebraic form (x is your number)
2x-11=7
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204 divided by 102 which is 2
306 divided by 102 which is 3

So the answer is 2/3

3 0
3 years ago
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