Answer: Please see attachment.
Solution:
We need to match the column using column proof. Please see the attachment for matching column.
In ΔDOC and ΔBOA
DO=BO (Given)
∠DOC=∠BOA (Vertically Opposite angle)
OC=OA (Given)
∴ ΔDOC ≅ ΔBOA by SAS congruence property
∠1=∠2 and AB=DC By CPCTE
Thus, AB||DC (∠1 and ∠2 are alternate angles equal then lines parallel)
ABCD is a parallelogram. ( If two sides equal and parallel then a parallelogram.
Below is matched table.
DO = OB, AO = OC ⇒ Given
∠ DOC =∠ AOB ⇒ Vertical angles are equal
∆COD ≅ ∆AOB ⇒ SAS CPCTE
∠1 = ∠2, AB = DC ⇒ CPCTE
AB||DC ⇒ If alternate interior angles =, then lines parallel
ABCD is a parallelogram ⇒ If two sides = and ||, then a parallelogram
Please see attachment for figure and matching.
Answer:
y = -3x
Step-by-step explanation:
(a) Slope
y = mx + b
Choose points (-3, 9) and (3, -9)
m = (-9 - 9)/(3 – (-3))
m = -18/(3 + 3)
m = -18/6
m = -3
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(b) y-intercept
y = mx +b
Choose point (0,0).
0 = 0 + b
b = 0
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(c) Equation of line
y = mx + b
y = -3x
<h3>
Answers:</h3>
- ST = 23
- RU = 8
- SV = 5
- SU = 10
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Explanation:
Focus on triangles SVT and UVT.
They are congruent triangles due to the fact that SV = VU and VT = VT. From there we can use the LL (leg leg) theorem for right triangles to prove them congruent.
Since the triangles are the same, just mirrored, this means ST = UT = 23.
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Following similar reasoning as the previous section, we can prove triangle RVU = triangle RVS.
Therefore, RS = RU = 8
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SV = VU = 5 because RT bisects SU.
Bisect means to cut in half. The two smaller pieces are equal.
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SU = SV + VU = 5+5 = 10
Refer to the segment addition postulate.