Hi there! Sorry to bother you, but can someone help me out with this? (the no. 7 to 10 pweassee) ฅ^•ﻌ•^ฅ For those who know the answer for this, please, can you help me? THANKSSS

Kindly explain your answers, i would rlly appreciate if you put an explanation for your answers

Please answer this correctly :'(

No links!

THANK YOUU VERYY MUCHH IN ADVANCE FOR WHOM WILL ANSWER MY QUESTIONS CORRECTLY =)

Unhelpful answer will be deleted ❌

Correct answer + with explanation will be chosen as the Brainliest Answer ✅​​​​

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  7. (question is nonsense)

  8.  B. substitution

  9.  A. AB=AB

  10.  B. substitution

Step-by-step explanation:

7. Consider ...

  Reflexive property: m∠D = m∠D

  Subtraction property: If m∠D +m∠E = m∠F +m∠E, then m∠D = m∠F

  Symmetric property: If m∠D = m∠F, then m∠F = m∠D

  Transitive property: if m∠D = m∠E and m∠E = m∠F, then m∠D = m∠F

Perhaps the intended expression is one that matches the Transitive property. We cannot tell. As written, the question is nonsense.

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8. The Substitution Property says that the equality of EF and DE means that we can replace DE with EF. That appears to be what has been done here. The Transitive Property says essentially the same thing, but is usually written differently.

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9. The Reflexive Property says an object is equal to itself, as shown in selection A:

  AB = AB

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10. Again, the Substitution Property says we can replace anything with its equal.

Problem 7

This question is bit weirdly worded.

If your teacher meant to say

If m < D = m < E and m < D = m < F, then m < D = m < F

then it seems a bit redundant since the last two parts just repeat themselves. There's not much to do or say. We have "m < D = m < F" already given so there's not much to prove.

If your teacher meant to say this instead

If m < D = m < E and m < E = m < F, then m < D = m < F

then that would make more sense. However, notice how I'm effectively rewriting the problem at this point. I'm making an assumption that may not be what your teacher intended to say/write.

If we assume your teacher meant to say the second concept mentioned above, then we would use the transitive rule. We have D connect to E which connects to F. In short, we start at D and end with F. Think of it like a band touring various cities. Or you can think of it like chaining together links. Or you could use arrow notation like so

If D -> E and E -> F, then D -> F

Again, I'm making an assumption that may not be what your teacher intended. Your teacher may have something entirely different in mind.

Problem 8

Thankfully this problem is better worded without any ambiguity or typos.

We're given that AB = DE and EF = DE are the two premises. They then lead to the conclusion that AB = EF.

How can we prove this? Through substitution. The second premise says that EF and DE are the same thing. So we could replace the "DE" in the first premise with "EF". Think of a substitute teacher and how they replace a regular teacher on a temporary basis.

Substitution comes up again in problem 10

Problem 9

Think of a mirror how it gives off a reflection. This is how I remember what the reflexive property is. When looking at your reflection, you're looking at yourself. So the reflexive property is the idea that any mathematical object is the same as itself. This is admittedly rather vague. What do I mean by "object"? Well it could apply to a lot of concepts in math, but with geometry we're concerned with angle measures and line segment lengths.

Writing AB = AB seems trivial, but it could be useful for a proof somehow (usually when we break up a figure into smaller pieces). Saying that equation uses the reflexive property since AB is the same length as itself.

Problem 10

Like I mentioned in problem 8, the substitution property comes up again.

This time we're replacing AB with 8. This is valid due to the first premise saying AB = 8, so AB and 8 are the same thing in this context.

So this is what our steps would look like

AC = AB + BC

AC = 8 + BC