Given: bisects ∠MRQ; ∠RMS ≅ ∠RQS
2 answers:
Answer:
ΔRMS ≅ ΔRQS by AAS
Step-by-step explanation:
See the diagram attached.
Given that ∠ RMS = ∠ RQS and N is any point on RS and ∠ MRS = ∠ SRQ.
Therefore, between Δ RMS and Δ RQS, we have
(i) ∠ RMS = ∠ RQS {Given}
(ii) ∠ MRS = ∠ SRQ {Also given} and
(iii) RS is the common side.
So, by angle-angle-side i.e. AAS criteria we can write ΔRMS ≅ ΔRQS. (Answer)
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Given:
The x- intercepts of a parabola are (0,-6) and (0,4).
The parabola crosses the y- axis at -120.
Lucas said that an equation for the parabola is and that the coordinates of the vertex are (-1, -125).
To find:
Whether Lucas is correct or not.
Solution:
The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.
...(i)
The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).
Divide both sides by -24.
Substituting in (i), we get
So, the equation of the parabola is .
The vertex of a parabola is:
In the equation of the parabola, .
Putting in the equation of the parabola, we get
So, the vertex of the parabola is at point (-1,-125).
Therefore, Lucas is correct.