triangle similarity

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rachelmaddie

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I need help with the side side side theorem

it says to give a congruency statement and reasoningA25731A3-5013-4C05-BDDF-BDE569B5048A.png
 
For congruency, SSS means all three pairs of corresponding sides are the same length. Is that the case?
Writing the left triangle as ABC, what order should you write the second triangle?
 
rachelmaddie said:
I need help with the side side side theorem

it says to give a congruency statement and reasoningView attachment 15306
Click to expand...
Some of your notation is incorrect.
\(\displaystyle \angle BAC\) is congruent to \(\displaystyle \angle BDC\) written as \(\displaystyle \angle BAC\cong\angle BDC\) however \(\displaystyle \angle BAC\ne\angle BDC\). To say equal to means they are the same angle.
You are to write congruencey statement: \(\displaystyle \Delta BAC\cong\Delta BDC\) Notice the order of the letters in each triangle.
If we see \(\displaystyle \Delta XYZ\cong\Delta BDC\) we know from the notation what corresponds to what.
\(\displaystyle \angle X \leftrightarrow \angle B\), \(\displaystyle \angle Y \leftrightarrow \angle D\), & \(\displaystyle \angle Z \leftrightarrow \angle C\)
Moreover, it must be the case that \(\displaystyle \overline{XZ}\cong\overline{BC}\); reading just from the congruency statement.
 
pka said:
Some of your notation is incorrect.
\(\displaystyle \angle BAC\) is congruent to \(\displaystyle \angle BDC\) written as \(\displaystyle \angle BAC\cong\angle BDC\) however \(\displaystyle \angle BAC\ne\angle BDC\). To say equal to means they are the same angle.
You are to write congruencey statement: \(\displaystyle \Delta BAC\cong\Delta BDC\) Notice the order of the letters in each triangle.
If we see \(\displaystyle \Delta XYZ\cong\Delta BDC\) we know from the notation what corresponds to what.
\(\displaystyle \angle X \leftrightarrow \angle B\), \(\displaystyle \angle Y \leftrightarrow \angle D\), & \(\displaystyle \angle Z \leftrightarrow \angle C\)
Moreover, it must be the case that \(\displaystyle \overline{XZ}\cong\overline{BC}\); reading just from the congruency statement.
Click to expand...
How do I write this out in the correctly to show my work?
 
Give it a try yourself. You need to argue why the three sides are congruent.
 
pka said:
Some of your notation is incorrect.
\(\displaystyle \angle BAC\) is congruent to \(\displaystyle \angle BDC\) written as \(\displaystyle \angle BAC\cong\angle BDC\) however \(\displaystyle \angle BAC\ne\angle BDC\). To say equal to means they are the same angle.
You are to write congruencey statement: \(\displaystyle \Delta BAC\cong\Delta BDC\) Notice the order of the letters in each triangle.
If we see \(\displaystyle \Delta XYZ\cong\Delta BDC\) we know from the notation what corresponds to what.
\(\displaystyle \angle X \leftrightarrow \angle B\), \(\displaystyle \angle Y \leftrightarrow \angle D\), & \(\displaystyle \angle Z \leftrightarrow \angle C\)
Moreover, it must be the case that \(\displaystyle \overline{XZ}\cong\overline{BC}\); reading just from the congruency statement.
Click to expand...
Who’s notation is incorrect?
 
12)
triangle BAC = triangle BDC
Identical symbols show BA = BD and AC = DC
BC is a common side to both triangle BAC and triangle BDC (reflexive law).
The three sides of triangle BAC (BA, BC, DC) are congruent to the corresponding three sides of triangle BDC (BD, BC, DC)
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
By SSS(side side side), the two triangles are congruent
 
As for the "incorrect notation" issue (which I think was aimed at Hoosie): In your real copy, you would be using the proper symbols, but since it is not easy to enter them all here, you could just state at the beginning that you are using "=" for the congruency symbol, to keep people from objecting. Alternatively, since others have been using it, you could just copy the symbols, as I am doing here from what you quoted in post #10: ∠BAC≅∠BDC , ΔXYZ≅ΔBDC

So here is what you are saying, with the right symbols (except for the bars over segment names):

ΔBAC ≅ ΔBDC:​
Identical symbols show BA ≅ BD and AC ≅ DC​
BC is a common side to both ΔBAC and ΔBDC (reflexive law).​
The three sides of ΔBAC (BA, BC, DC) are congruent to the corresponding three sides of ΔBDC (BD, BC, DC)​
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.​
By SSS (side side side), the two triangles are congruent​

Very likely you aren't required to show that much detail; you'll have to ask your teacher about that. In writing proofs, we don't say that we can tell two segments are congruent by the markings on them; we just say that we are told they are congruent! But you're at the beginning of the learning process and not writing full proofs yet, so it's good to think through, and write out, all the details.

So try again if you like, not copying quite so much from Hoosie (e.g., your last two lines are synonymous, so one could be dropped). But this is a math help site, and this is verging on trying to make your English perfect. I'd move on.
 
Dr.Peterson said:
As for the "incorrect notation" issue (which I think was aimed at Hoosie): In your real copy, you would be using the proper symbols, but since it is not easy to enter them all here, you could just state at the beginning that you are using "=" for the congruency symbol, to keep people from objecting. Alternatively, since others have been using it, you could just copy the symbols, as I am doing here from what you quoted in post #10: ∠BAC≅∠BDC , ΔXYZ≅ΔBDC

So here is what you are saying, with the right symbols (except for the bars over segment names):

ΔBAC ≅ ΔBDC:​
Identical symbols show BA ≅ BD and AC ≅ DC​
BC is a common side to both ΔBAC and ΔBDC (reflexive law).​
The three sides of ΔBAC (BA, BC, DC) are congruent to the corresponding three sides of ΔBDC (BD, BC, DC)​
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.​
By SSS (side side side), the two triangles are congruent​

Very likely you aren't required to show that much detail; you'll have to ask your teacher about that. In writing proofs, we don't say that we can tell two segments are congruent by the markings on them; we just say that we are told they are congruent! But you're at the beginning of the learning process and not writing full proofs yet, so it's good to think through, and write out, all the details.

So try again if you like, not copying quite so much from Hoosie (e.g., your last two lines are synonymous, so one could be dropped). But this is a math help site, and this is verging on trying to make your English perfect. I'd move on.
Click to expand...
Did I label the letters correctly?
 
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