Answer:
Step-by-step explanation:
Subtitute y in the first equation.
Now replace x in either equation to find y.
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Answer:
The sentence which accurately completes the proof is: "Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem." ⇒ 2nd answer
Step-by-step explanation:
Let us revise the cases of congruence
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
- HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ
In Parallelogram ABCD
∵ Segment AB is parallel to segment DC
∵ Segment BC is parallel to segment AD
- Construct diagonal A C with a straightedge
In Δs BCA and DAC
∵ AC is congruent to itself ⇒ Reflexive Property of Equality
∵ ∠BAC and ∠DCA are congruent ⇒ Alternate Interior Angles
∵ ∠BCA and ∠DAC are congruent ⇒ Alternate Interior Angles
- AC is joining the congruent angles
∴ Δ BCA is congruent to Δ DAC by ASA Theorem of congruence
By CPCTC
∴ AB is congruent to CD
∴ BC is congruent to DA
The sentence which accurately completes the proof is: "Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem."
Hope this helps! Let me know if you need anything.
