What are the missing parts that correctly complete the proof?
Given: point P is on the bisector of ABC.
Prove: point P is equidistant from the sides of ABC.
1. BP is the bisector of ABC- given
2. ABP≈CBP- ?
3. BXP and BYP are right angles- given
4. ?- all right angles are congruent
5. BP≈BP- ?
6. BXP≈BYP- ?
7. ?- corresponding parts of congruent triangles are congruent
8. Point P is equidistant from the sides of ABC- definition of equidistant
Answers
Answer:
Hello, I just took the test today. I will attach a screenshot. I hope I am not too late answering your question.
This question stumped me too at first. I hope this helps!
The missing parts that correctly complete the proof are;
2) Definition of a bisector
4) ∠BXP ≅ ∠BYP.
5) Reflexive property of congruence.
6) AAS congruence theorem.
7) Corresponding sides of congruent triangles are congruent.
We are given;
Point P is on the bisector of ∠ABC.
2) ∠ABP ≅ ∠CBP; The symbol ≅ means congruent. This means they are equal and it is true because it corresponds with the definition of a bisector means dividing into 2 equal parts.4) All right angles are congruent; Congruent means equal and the two right angles we have in the image are; ∠BXP and ∠BYP. Thus, we can write; ∠BXP ≅ ∠BYP.5) BP ≅ BP; This means that Line BP is congruent and equal to itself and this fulfils the theorem called reflexive property of congruence.6) ΔBXP ≅ ΔBYP; This means ΔBXP is congruent to ΔBYP. Since we have established that ∠BXP ≅ ∠BYP; ∠ABP ≅ ∠CBP; BP ≅ BP. It means we have 2 corresponding angles and one corresponding side equal to each other from the 2 congruent triangles and so we can say this fulfils the AAS congruence theorem.7) PX ≅ PY; This means PX is congruent to PY. From congruence theorem, corresponding sides of congruent triangles are congruent.
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Answer:
21n-35
Step-by-step explanation:
6n+5(10n-7)
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Step-by-step explanation:
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Step-by-step explanation:
Given a 30-60-90 triangle with a hypotenuse of 11 mm solve for the other sides. (Explain)
Answers
Answer:
Need a calculator
Step-by-step explanation:
This will be hard to explain without the ability to draw an example.
The one thing you can memorize is SOH - CAH - TOA
This stands for SIN(Opposite/Hypotenuse), COS(Adjacent/Hypotenuse) and TAN(Opposite/Adjacent).
When you know the angles of a right triangle and at least one side length, you can get the length of all the sides.
So a right triangle has two legs (sides) and the hypotenuse. If you use the first angle ( 30 degrees) you can use the formulas above to calculate the side length.
Pick either the SOH or the CAH. Let's use SOH and write out the equation:
SIN(30 degrees) = Opposite Side divided by the Hypotenuse (11mm)
You can solve for the Opposite Side by multiplying both sides of the equal sign with 11mm. You end up with SIN(30 degrees) X 11m = Opposite Side.
So the side directly across from the 30 degree angle should be 5.5mm
You can do the exact same thing with the 60 degree angle.
SIN(60 degrees) = Opposite Side divided by Hypotenuse (11mm) OR
SIN(60 degrees) X 11mm = Opposite Side
This comes out to about 9.5mm
You can check the math by using the other equation CAH
Start with the 30 degree angle and solve for the adjacent side. This is the side that is touching the 30 degree angle. Equation will be
COS(30 degrees) X 11mm = Adjacent Side or about 9.5mm
The other equation will give you the side that is touching the 60 degree angle.
COS(60 degrees) X 11mm = Adjacent Side or 5.5mm
You can also use one last thing to check your math. The Pathagorean Theorem says in a right triangle [tex]A^{2}[/tex] + [tex]B^{2}[/tex] = [tex]C^{2}[/tex] where C is the hypotenuse and A and B are the two sides.
[tex]5.5^{2}[/tex] + [tex]9.5^{2}[/tex] should equal [tex]11^{2}[/tex]. Give or take a few decimal places, it's almost exactly 11 (10.977 to be exact).
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Answers
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Step-by-step explanation:
Answer:
Step-by-step explanation:
Simplifying
14 + x = 3a + ab
Solving
14 + x = 3a + ab
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + x = 3a + -14 + ab
Combine like terms: 14 + -14 = 0
0 + x = 3a + -14 + ab
x = 3a + -14 + ab
Reorder the terms:
x = -14 + 3a + ab
Simplifying
x = -14 + 3a + ab
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
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Step-by-step explanation:
For Plato users
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Step-by-step explanation:
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Step-by-step explanation:
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Answer
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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